Multiple solutions for systems with singular ϕ-Laplacian operator
PN-III-P1-1.1-PD-2016-0040
Funding Sources: Uniunea Executivă pentru Finanțarea Învățământului Superior, a Cercetării Dezvoltării și Inovării
Consiliul Național al Cercetării Științifice
Grant no.: 9/2018
Title (in romanian): "Soluții multiple pentru sisteme cu operator ϕ-Laplacian singular"
Domains: Theoretical aspects of partial differential equations, ODE and dynamical systems
Team: Călin - Constantin ȘERBAN (project leader) - calin.serban@e-uvt.ro, cserban2005@yahoo.com ;
Cornelia VIZMAN (mentor)
Host Institution: West University of Timișoara
Contract Period: 02/05/2018 - 30/04/2020
Budget Breakdown: 250.000 RON (estimated budget for the entire period of the grant)
Abstract
This research project focus on boundary value problems for partial differential systems, as well as for differential systems with singular ϕ-Laplacians. The prototype for such Laplacians is the mean curvature operator in Minkowski space which has significant importance in differential geometry and special relativity. We intend to obtain multiplicity of solutions for singular ϕ-Laplacians systems subjected to Dirichlet, periodic or Neumann boundary conditions. In order to prove the expected results one make use of variational and/or topological methods.
Project General Objective
We intend to obtain existence and multiplicity of various type of solutions (nontrivial, non-negative, positive, etc.) for systems involving the relativistic operator and the mean curvature operator in Minkowski space with different type of nonlinearities and subjected to periodic, Dirichlet and/or Neumann boundary conditions. The results we intend to obtain will be published in prestigious journals and also will be presented to international conferences in the field.
Project General Plan
Phase I (2018 - 8 months) - Existence and multiplicity for Dirichlet systems with mean curvature operator in Minkowski space (cf. Objective 3 of the Funding Application)
Phase II (2019 - 12 months) - Existence and multiplicity for Neumann systems with mean curvature operator and relativistic operator I (cf. Objectives 1 & 2 of the Funding Application)
Phase III (2020 - 4 months) - Existence and multiplicity for Neumann systems with mean curvature operator and relativistic operator II (cf. Objectives 1 & 2 of the Funding Application)
Estimated Results
The estimated results aim the existence and multiplicity of solutions for systems with mean curvature operator in Minkowski space which will extend the results already obtained in the literature for one equation. Also, we intend to obtain the existence of geometrically distinct solutions for the relativistic pendulum system when the nonlinearity is not periodic in all variables; these could also concern systems with different p and q-relativistic operators. We also have in view to extend the lower and upper solution method for Dirichlet systems with mean curvature operator in Minkowski space on a general bounded domain. These would allow by topological degree or fixed point index arguments to show the existence, multiplicity and localization of solutions for such systems. In addition, an interesting aspect (known in the case of some classical divergence operators) is the diagram in the first quadrant of the parameters drawing the areas of non-existence, existence and multiplicity of positive solutions of parameterized systems with Lane-Emden nonlinearities. The expected verifiable results of the project are the submission for publication to ISI ranked Journals of three articles and the participation to at least five international conferences/workshops organized abroad/in Romania.
ISI (RED Zone) Journals
D. Gurban, P. Jebelean, C. Șerban, Non-potential and non-radial Dirichlet systems with mean curvature operator in Minkowski space, Discrete Contin. Dyn. Syst. A* 40 (1) (2020), 133-151, DOI: 10.3934/dcds.2020006, WOS: 000496748500006 (submitted: 12 November 2018; accepted: 3 July 2019) [link | .pdf file] - article awarded by UEFISCDI in the “National Plan for Research, Development and Innovation - Awarding of research results” - PRECISI 2020 (RED Zone).
P. Jebelean, J. Mawhin, C. Șerban, Multiple critical orbits to partial periodic perturbations of the p-relativistic operator, Appl. Math. Lett.** 104 (2020), ID: 106220, DOI: 10.1016/j.aml.2020.106220, WOS: 000521510800008 (submitted: 23 November 2019; accepted: 6 January 2020) [link | .pdf file] - article awarded by UEFISCDI in the “National Plan for Research, Development and Innovation - Awarding of research results” - PRECISI 2020 (RED Zone).
A. Chinni, B. Di Bella, P. Jebelean, C. Șerban, Periodic solutions for systems with p-relativistic operator and unbounded discontinuous nonlinearities, Mediterr. J. Math.*** 18 (22) (2021), DOI: 10.1007/s00009-020-01662-9 (submitted: 13 August 2019; accepted: 31 May 2020). [link | .pdf file]
P. Jebelean, C. Șerban, Fisher-Kolmogorov type perturbations of the mean curvature operator in Minkowski space, Electron. J. Qual. Theory Differ. Equ.**** 81 (2020), 1-12, DOI: 10.14232/ejqtde.2020.1.81 (submitted: 5 August 2020; accepted: 10 September 2020) -- initial preprint title which appear on the Phase III report as work in progress: "Multiple non-radial solutions for Dirichlet problems with mean curvature operator" [link | .pdf file]
*Discrete and Continuous Dynamical Systems - A (DCDS-A), ISSN: 1078-0947 – IF: 1.143; AIS: 0.968; SRI: 1.541, cf. JCR-2018 (June 2019) - Source or Scientometrie UEFISCDI, Web of Science Categories: Mathematics; Mathematics, Applied – RED Zone (IF-Mathematics & AIS-Mathematics, Applied) & YELLOW Zone (AIS-Mathematics & IF-Mathematics, Applied).
**Applied Mathematics Letters, ISSN: 0893-9659 – IF: 3.487; AIS: 0.842; SRI: 1.305, cf. JCR-2018 (June 2019) - Source or Scientometrie UEFISCDI, Web of Science Categories: Mathematics, Applied – RED Zone (IF-Mathematics, Applied) & YELLOW Zone (AIS-Mathematics, Applied).
***Mediterranean Journal of Mathematics, ISSN: 1660-5446 – IF: 1.181; AIS: 0.36; SRI: 0.573, cf. JCR-2018 (June 2019) - Source or Scientometrie UEFISCDI, Web of Science Categories: Mathematics; Mathematics, Applied – RED Zone (IF-Mathematics) & YELLOW Zone (IF-Mathematics, Applied).
****Electronic Journal of Qualitative Theory of Differential Equations, ISSN: 1417-3875 – IF: 1.827; AIS: 0.448; SRI: 0.722, cf. JCR-2019 (June 2020) - Source or Scientometrie UEFISCDI, Web of Science Categories: Mathematics; Mathematics, Applied – RED Zone (IF-Mathematics).
Related ISI publications
C. Șerban, Multiple solutions of Neumann systems of relativistic-type, Minimax Theory and its Applications 3 (1) (2018), 47-56. [link | .pdf file]
P. Jebelean, C. Şerban, Fisher-Kolmogorov type perturbations of the relativistic operator: differential vs difference, Proc. Amer. Math. Soc. 146 (2018), 2005-2014 [link | .pdf file] - article awarded by UEFISCDI in the “National Plan for Research, Development and Innovation - Awarding of research results” - PRECISI 2018 (YELLOW Zone).
*These two papers include results very closely related to the theme and objectives of the project, but they do not contain the mention of the project because they were published before the contract was signed. This situation appeared because the evaluation period (between sending the Funding Application and signing the contract) was very long and did not respect the calendar, and so it was delayed by almost a year.
International Conferences abroad
Equadiff 2019, Session CT22: Special solutions, July 8-12, 2019, Leiden University, The Netherlands, title of the talk: Strictly positive solutions for non-potential and non-radial Dirichlet systems with Minkowski operator (Site | Certificate | Info Program CT22 & Index | Program | Abstracts (p. 97))
International Conference on Differential and Difference Equations and Applications 2019 (ICDDEA-2019), Special Session: Variational, Topological and Set-Valued Methods for nonlinear boundary value problems, July 1-5, 2019, Lisbon, Portugal, title of the talk: Periodic solutions for systems with p-relativistic operator and unbounded discontinuous nonlinearities (Site | Certificate | Program | Abstracts (p. 123))
Italian-Romanian Colloquium on Differential Equations and Applications, April 10-12, 2019, Università degli Studi di Udine, Italy, title of the talk: Non-radial multiparameter Dirichlet systems with Minkowski operator (Site | Poster | Certificate | Program | Abstracts (p. 7))
International Conference in Nonlinear Analysis and Boundary Value Problems 2018 (NABVP-2018), Special Session: Boundary Value Problems, September 4-7, 2018, University of Santiago de Compostela, Spain, title of the talk: Multiple solutions for systems with mean curvature operator in Minkowski space (Site | Certificate | Program | Abstracts (p. 32))
The Seventh International Workshop-2018 ”Constructive methods for non-linear boundary value problems”, July 5-8, 2018, Institute of Mathematics - University of Miskolc (Hungary) and Institute of Mathematics of the Academy of Sciences of the Czech Republic, Miskolc, Hungary, title of the talk: Multiple solutions for systems with singular operator (Site | Certificate | Program)
Veszprém Conference on Differential and Difference Equations and Applications (VCDDEA 2018), July 2-5, 2018, University of Pannonia, Veszprém, Hungary, title of the talk: Some multiplicity results for boundary value problems with singular ϕ-Laplacian (Site | Certificate | Program | Abstracts (p. 29))
International Conferences in Romania
The Ninth Congress of Romanian Mathematicians (CRM9), Section: Ordinary and Partial Differential Equations, Controlled Differential Systems, June 28 - July 3, 2019, Galați, Romania, title of the talk: Existence of periodic solutions for unbounded discontinuous perturbations of the p-relativistic operator (Site | Certificate | Program | Abstracts (p. 79))
The 15th International Conference on Mathematics and its Applications (ICMA 2018), Session: Mathematical Analysis and Applications, November 1-3, 2018, Politehnica University of Timișoara and Romanian Academy - Branch Timișoara, Romania, title of the talk: Multiple periodic solutions for differential and difference equations with relativistic operator (Site | Certificate | Program | Abstracts (p. 8))
International Workshop ”Geometry and PDEs” 2018, 5th Edition, Session: PDEs, October 12-13, 2018, West University of Timișoara, Romania, title of the talk: Non-radial, non-potential systems with Minkowski operator (Site | Certificate | Program)
Workshop for Young Researchers in Mathematics, 8th Edition, May 17-18, 2018, ”Simion Stoilow” Institute of Mathematics of the Romanian Academy, Bucharest, Romania, title of the talk: Periodic solutions for differential and difference equations involving Fisher-Kolmogorov perturbations of the relativistic operator (Site | Certificate | Program | Abstracts)
Workshop Organized
International Workshop ”Geometry and PDEs” 2018, 5th Edition, October 12-13, 2018, West University of Timișoara, Romania, co-organizer of Section ”PDEs” (Site | Poster)