PN-II-ID-PCE-2011-3-0557 Grant

PROJECT TITLE

BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS WITH APPLICATIONS IN ELECTRONICS AND MECHANICS 

COD PN-II-ID-PCE-2011-3-0557, CONTRACT NR.155/05.10.2011, ANCS-CNCS-UEFISCDI

ABSTRACT OF THE PROJECT

We study the existence, multiplicity and nonexistence of positive solutions for some systems of second-order or higher-order nonlinear ordinary differential equations subject to various multi-point boundary conditions, which have applications in engineering, physics and life sciences. In the systems, the nonlinearities are non-singular or singular functions. Some discrete cases of the above problems are also investigated.

We also study some nonlinear hyperbolic systems with boundary conditions which contain extra-functions and initial conditions. We are interested in the existence, uniqueness, regularity properties and asymptotic properties of the weak and strong solutions. These problems are models for some processes in electronics, mechanics, hydraulics and gas-dynamics.

We study the modelling and stability of crop-pest-pathogen models with evolutionary response of defence mechanics. Finite time control strategies for impulsive functional differential equations and applications to integrated pest management are also investigated.

Keywords: boundary value problems, systems of differential equations, systems of difference equations, boundary conditions, multi-point boundary conditions, stability, permanence, impulsive controls.

Contract data:

Financing: State budget

Program name of PN-II: IDEI

Subprogram: Exploratory research

Duration of contract: 60 months (October 5, 2011 - October 5, 2016)

Authority: Executive Agency for Higher Education, Research, Development and Innovation Funding

Contractor: "Gheorghe Asachi" Technical University of Iasi

Team:

Prof. dr. Rodica Luca Tudorache

Assoc. prof. dr. (Prof. dr. - since 2015) Valeriu-Paul Georgescu 

Assist. prof. drd. (Assist. prof. dr. - since 2014) Ciprian Deliu (until June 30, 2014)

Stud. Alexandru-Gabriel Tudorache (since July 1, 2014)

Scientific activity 2011 

1. Johnny Henderson, Rodica Luca, Positive solutions for a system of higher-order multi-point boundary value problems, Computers and Mathematics with Applications, 62 (2011), 3920-3932, (ISI).

2. Rodica Luca, Existence and uniqueness of solutions for a second-order nonlinear hyperbolic system, Electronic Journal of Differential Equations, Vol. 2011 (2011), No.78, pp. 1-11, (ISI).

3. Rodica Luca, Existence of positive solutions for a second-order m+1-point discrete boundary value problem, Journal of Difference Equations and Applications, DOI: 10.1080/10236198.2010.524213, (published in 2012), 18(5) (2012), 865-877, (ISI).

4. Rodica Luca, Boundary value problems for nonlinear systems with generalized second-order differences, Carpathian Journal of Mathematics, 27 (2011), 95-104, (ISI).

5. Rodica Luca, Positive solutions of m-point boundary value problems for systems of nonlinear second-order differential equations, Analele Ştiinţifice ale Universităţii „Al.I.Cuza” din Iaşi, Matematica, Tomul LVII,  Supliment (2011), 161-174, (ISI).

6. Rodica Luca, Positive solutions for a second-order m-point boundary value problem, Dynamics of Continuous, Discrete and Impulsive Systems, 18 (2011), 161-176, (International Databases IDB).

For the abstracts of the above papers and other activities, see the attached file: Report_2011.pdf

Scientific activity 2012 

1. Johnny Henderson, Rodica Luca, Positive solutions for a system of second-order multi-point boundary value problems, Applied Mathematics and Computation, 218 (2012), 6083-6094, (ISI).

2. Johnny Henderson, Rodica Luca, Existence and multiplicity for positive solutions of a multi-point boundary value problem, Applied Mathematics and Computation, 218 (2012), 10572-10585, (ISI).

3. Johnny Henderson, Rodica Luca, On a system of second-order multi-point boundary value problems, Applied Mathematics Letters, 25 (2012), 2089-2094, (ISI).

4. Johnny  Henderson, Rodica Luca, Positive solutions for singular systems of multi-point boundary value problems, Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.2628, (ISI), (published in 2013),  36 (7) (2013), 814-828, (ISI).

5. Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of higher-order multi-point boundary value problems, Applied Mathematics and Computation, 219 (2012), 3709-3720, (ISI).

6. Johnny Henderson, Rodica Luca, Positive solutions for a system of second-order multi-point discrete boundary value problems, Journal of Difference Equations and Applications, 18(9) (2012), 1575-1592, (ISI).

7. Johnny Henderson, Rodica Luca, Existence and multiplicity for positive solutions of a second-order multi-point discrete boundary value problem, Journal of Difference Equations and Applications, DOI: 10.1080/10236198.2011.648187, (published in 2013) 19 (3) (2013), 418-438, (ISI).

8. Johnny Henderson, Rodica Luca, On a system of higher-order multi-point boundary value problems, Electronic Journal of Qualitative Theory of Differential Equations, 49 (2012), 1-14, (ISI).

9. Rodica Luca, Positive solutions for a higher-order m-point boundary value problem, Mediterranean Journal of Mathematics, 9 (2012), 379-392, (ISI).

10. Rodica Luca, On a higher-order m-point boundary value problem, Fixed Point Theory, 13 (2012), 137-145, (ISI).

11. Paul Georgescu, Hong Zhang,  An impulsively controlled pest management model with n predator species and a common prey, BioSystems, 110 (2012), 162-170, (ISI).

12. Hong Zhang, Paul Georgescu,  Finite-time control of impulsive hybrid dynamical systems in pest management, accepted to Mathematical Methods in the Applied Sciences, (published in 2014), 37 (2014), 2728--2738, (ISI).

13. Rodica Luca, On a class of m-point boundary value problems, Mathematica Bohemica, 137(2) (2012), 187-194, (ISI).

14. Rodica Luca, Ciprian Deliu, Existence of positive solutions for a higher-order multi-point boundary value problem, Romai Journal, 8 (2), 143-152 (2012), (IDB).

15. Johnny Henderson, Rodica Luca, Existence of positive solutions for a nonlinear higher-order multi-point boundary value problem, Bulletin of the Transilvania University of Braşov, Series III: Mathematics, Informatics, Physics, Vol. 5(54) (2012), 167-178, (IDB).

16. Johnny Henderson, Rodica Luca, Positive solutions for second-order multi-point discrete boundary value problems, in "Numerical Analysis and Applied Mathematics ICNAAM 2012, International Conference of Numerical Analysis and Applied Mathematics", Kos, Greece, 19-25 September 2012, Series: AIP Conference Proceedings, Vol. 1479, T.E. Simos, G. Psihoyios, C. Tsitouras, Z. Anastassi, (Eds.), 565-567, 2013, (ISI Proceedings).

For the abstracts of the above papers and other activities, see the attached file: Report_2012.pdf

Scientific activity 2013 

1. Johnny Henderson, Rodica Luca, Positive solutions for systems of nonlinear second-order multi-point boundary value problems, Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.2993,  (published in 2014), 37 (2014), 2502-2516, (ISI).

2. Johnny Henderson, Rodica Luca, Positive solutions for a system of second-order nonlinear multi-point eigenvalue problems, Applied Mathematics and Computation, 223 (2013), 197-208, (ISI).

3. Johnny Henderson, Rodica Luca, Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems, Nonlinear Differential Equations and Applications, 20 (3) (2013), 1035-1054, (ISI).

4. Johnny Henderson, Rodica Luca, Positive solutions for singular systems of higher-order multi-point boundary value problems, Mathematical Modelling and Analysis, 18 (3) (2013), 309-324, (ISI)

5. Johnny Henderson, Rodica Luca, On a multi-point discrete boundary value problem, Journal of Difference Equations and Applications, 19 (4) (2013), 690-699, (ISI).

6. Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of second-order multi-point discrete boundary value problems, Journal of Difference Equations and Applications, 19 (11), (2013), 1889-1906, (ISI).

7. Johnny Henderson, Rodica Luca, Positive solutions for a system of nonlocal fractional boundary value problems, Fractional Calculus and Applied Analysis, 16 (4), (2013), 985-1008, (ISI).

8. Paul Georgescu, Hong Zhang, Lyapunov functionals for two-species mutualisms, Applied Mathematics and Computation, accepted for publication, (published in 2014), 226 (2014), 754--764, (ISI).

9. Johnny Henderson, Rodica Luca, Existence and multiplicity of positive solutions for a system of higher-order multi-point boundary value problems, Advances in Dynamical Systems and Applications, 8 (2) (2013), 233-245, (IDB).

10. Rodica Luca, Ciprian Deliu, Nonexistence of positive solutions for a system of higher-order multi-point  boundary value problems, Romai Journal, 9 (1) (2013), 69-77, (IDB).

11. Paul Georgescu, Hong Zhang, Permanence, periodicity and stability for an impulsively perturbed single species model, Buletinul Institutului Politehnic Iasi, (published in 2014), LX (LXIV) (2014), Issue 2, Section Mathematics, Theoretical Mechanics, Physics, 97--109, (IDB).

12. Johnny Henderson, Rodica Luca, Multiple positive solutions for a second-order multi-point discrete boundary value problem, AIP Conference Proceedings "11th International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2013", September 21-27, 2013, Rhodes, Greece, Vol. 1558, Editors: Theodore Simos, Georgios Psihoyios and Charalambos Tsitouras, 391 (2013), pp. 391-394, doi: 10.1063/1.4825506, (Proceedings ISI).

For the abstracts of the above papers and other activities, see the attached file: Report_2013.pdf

Scientific activity 2014 

1. Johnny Henderson, Rodica Luca, Positive solutions for systems of second-order integral boundary value problems, Electronic Journal of Qualitative Theory of Differential Equations, 2013:70 (2013), pp. 1-21 (published in December 2013),  (ISI).

2. Johnny Henderson, Rodica Luca, On a second-order nonlinear discrete multi-point eigenvalue problem, Journal of Difference Equations and Applications,  20 (7) (2014), 1005-1018, (ISI).

3. Johnny Henderson, Rodica Luca, Existence and multiplicity of positive solutions for a system of fractional boundary value problems, Boundary Value Problems, 2014:60 (2014), pp. 1-17, (ISI).

4. Rodica Luca, Alexandru Tudorache, Positive solutions to a system of semipositone fractional boundary value problems, Advances in Difference Equations, 2014:179 (2014), pp.1-11, (ISI).

5. Johnny Henderson, Rodica Luca, Positive solutions for a system of fractional differential equations with coupled integral boundary conditions, Applied Mathematics and Computation, 249 (2014), 182-197, (ISI).

6. Mouffak Benchohra, Johnny Henderson, Rodica Luca, Abdelghani Ouahab, Boundary data smoothness for solutions of second order ordinary differential equations with integral boundary conditions, Dynamic Systems and Applications, 23 (2014), 133-144, (ISI).

7. Hong Zhang, Paul Georgescu, Hassan Adamu Shitu, Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito, accepted to Applied Mathematics and Computation,  (published in 2016), 273 (2016), 1059-1089, (ISI).

8. Johnny Henderson, Rodica Luca, Positive solutions for systems of multi-point nonlinear boundary value problems, Communications on Applied Nonlinear Analysis, 21 (3) (2014), 1-12, (IDB).

9. Johnny Henderson, Rodica Luca, Comparison of smallest eigenvalues for certain third order boundary value problems, PanAmerican Mathematical Journal, 24 (3) (2014), 75-81, (IDB).

10. Johnny Henderson, Rodica Luca, Positive solutions for systems of singular higher-order multi-point boundary value problems, British Journal of Mathematics & Computer Science, 4 (4) (2014), 460-473, (IDB).

11. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Multiple positive solutions for a second-order multi-point boundary value problem, Romai Journal, 10 (1) (2014), 71-80, (IDB)

12. Ciprian Deliu, Ion Giurma, Data assimilation applications in hydrology, Buletinul Institutului Politehnic din Iaşi, Construcţii. Arhitectură, Tomul LX (LXIV), Fasc.2 (2014), 93-101,(IDB).

13. Hong Zhang, Mingming Su, Paul Georgescu, The global dynamics and optimal control of a plant epidemic model, accepted to Communications in Mathematical Biology and Neuroscience, (published in 2015), vol. 2015 (2015), Article ID 32, 1--18, (IDB). 

For the abstracts of the above papers and other activities, see the attached file: Report_2014.pdf

For the evaluation of the project (in March 2014), see the attached file: Fisa de evaluare a stadiului implementarii - LUCA TUDORACHE RODICA.pdf, in which the project received the best mark A+.

Scientific activity 2015 

1. Johnny Henderson, Rodica Luca, Alexandru Tudorache, On a system of fractional differential equations with coupled integral boundary conditions, Fractional Calculus and Applied Analysis, 2015, 18 (2), 361-386, (ISI).

2. Johnny Henderson, Rodica Luca, Nonexistence of positive solutions for a system of coupled fractional boundary value problems, Boundary Value Problems, 2015, 2015:138, pp. 1-12, (ISI).

3. Johnny Henderson, Rodica Luca, Positive solutions for systems of second-order difference equations, Discrete Dynamics in Nature and Society, 2015, Volume 2015, Article ID 468648, pp. 1-8, (ISI).

4.  John Graef, Johnny Henderson, Rodica Luca, Yu Tian, Boundary value problems for third order Lipschitz ordinary differential equations, Proceedings of  the Edinburg Mathematical Society,  2015, 58 (1), 183-197, (ISI).

5.  Johnny Henderson, Rodica Luca, Positive solutions for a system of difference equations with coupled multi-point boundary conditions, Journal of Difference Equations and Applications, 2016, 22 (2), 188-216,  (ISI).

6. Hong Zhang, Juan Xia, Paul Georgescu, Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay, Nonlinear Analysis: Modelling and  Control, 2017, 22 (1), 64-83, (ISI).

7. Daniel Maxin, Paul Georgescu, Laurenţiu Sega, Ludek Berec, Global stability of the coexistence equilibrium for a general class of models of facultative mutualism, Journal of Biological Dynamics, 2017, 11, 339-364, (ISI).

8.  Rodica Luca, Alexandru Tudorache, Existence of positive solutions to a system of higher-order semipositone integral boundary value problems, Communications in Applied Analysis, 2015, 19, 589-604, (IDB).

9. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Positive solutions for a fractional boundary value problem, Nonlinear Studies, 2015, 22 (1), 1-13, (IDB).

10. Johnny Henderson, Rodica Luca, Charles Nelms Jr., Aijun Yang, Positive solutions for a singular third order boundary value problem, Differential Equations & Applications, 2015, 7 (4), 437-447, (ISI).

11. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Positive solutions for systems of coupled fractional boundary value problems, Open Journal of Applied Sciences, 2015, 5, 600-608, (IDB).

12.  Johnny Henderson, Rodica Luca, Alexandru Tudorache, Multiple positive solutions for a multi-point discrete boundary value problem, Communications, Faculty of Sciences, University of Ankara, Series A1: Mathematics and Statistics, 2014, 63 (2), 59-70, (published in 2015), (ISI).

13.  Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of nonlinear second-order integral boundary value problems, Dynamical Systems, Differential Equations and Applications, AIMS Proceedings, 2015 (Proceedings of the 10th AIMS International Conference, Madrid, Spain, 2014), 596-604, DOI:10.3934/proc.2015.0596.

14. Paul Georgescu, Daniel Maxin, Hong Zhang, Global stability results for models of commensalism, International Journal of Biomathematics, 2017 (10), 1750037 (25 pages), (ISI).

15. Monograph

Johnny Henderson, Rodica Luca, "Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions", Elsevier, Amsterdam, 2016 (2015 in Elsevier), 322 pages, ISBN: 978-0-12-803652-5, ( https://www.elsevier.com/books/boundary-value-problems-for-systems-of-differential-difference-and-fractional-equations/henderson/978-0-12-803652-5 ).

For the abstracts of the above papers and other activities, see the attached file: Report_2015.pdf

The above monograph was awarded the "Spiru Haret" Prize of the Romanian Academy, on December 2018.

Scientific activity 2016 

1. Johnny Henderson, Rodica Luca, Positive solutions for a system of semipositone coupled fractional boundary value problems, Boundary Value Problems, 2016, 2016:61, pp. 1-23, (ISI).

2. Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of semipositone fractional boundary value problems, Electronic Journal of Qualitative Theory of Differential Equations, 2016, No. 22, pp. 1-28, (ISI).

3. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Existence and nonexistence of positive solutions for coupled Riemann-Liouville fractional boundary value problems, Discrete Dynamics in Nature and Society, 2016, Vol. 2016, Article ID 2823971, 1-12, (ISI).

4. Johnny Henderson, Rodica Luca, Existence and multiplicity of positive solutions for a system of difference equations with coupled boundary conditions, Journal of Applied Analysis and Computation, 2017, 7 (1), 134-146, (ISI).

5. Johnny Henderson, Rodica Luca, On a system of Riemann-Liouville fractional boundary value problems, Communications on Applied Nonlinear Analysis, 2016, 23 (2), 1-19, (IDB).

6. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Positive solutions for a system of second-order differential equations with integral boundary conditions, International Journal of Applied Physics and Mathematics, 2016, 6 (3), 138-149, (IDB).

7. Johnny Henderson, Rodica Luca, Existence of positive solutions for a singular fractional boundary value problem, Nonlinear Analysis: Modelling and Control, 2017, 22 (1), 99-114, (ISI).

8. Johnny Henderson, Rodica Luca, Positive solutions for a system of singular second-order integral boundary value problems, Fixed Point Theory, 2018, 19 (1), 249-264, (ISI).

9. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Existence of positive solutions for a system of fractional boundary value problems, in „Differential and Difference Equations with Applications”, ICDDEA, Amadora, Portugal, May 2015, Selected Contributions, Editors: Sandra Pinelas, Zuzana Dosla, Ondrej Dosly, Peter E. Kloeden, (451 pag.), Springer, 2016, pag. 349-357, (ISI Proceedings).

10. Paul Georgescu, Daniel Maxin, Hong Zhang, Threshold boundedness conditions for n-species mutualisms, Nonlinearity, 2017, 30 (12) (ISI).

11. H. Zhang, F. Tian, P. Harvim, P. Georgescu, Effects of size refuge specificity on a predator-prey model, BioSystems, 2017, 152, 11-23, (ISI).

12. H. Zhang, P. Harvim and P. Georgescu, Preventing the spread of schistosomiasis in Ghana: the effects of integrated optimal control strategies, Journal of Biological Systems, 2017, 25 (4), 625-655 (ISI).

For the abstracts of the above papers and other activities, see the attached file: Report_2016.pdf