ferhan.atici@wku.edu
Western Kentucky University, USA
Title: Discrete Ponzi Scheme Model
Co-author(s): William Bennett
Abstract: In this paper, we introduce a second order self-adjoint difference equation which describes the dynamics of Ponzi schemes: a type of investment fraud that promises more than it can deliver. We use the Sturm-Liouville theory to study the discrete equation with boundary conditions. The model is based on a promised, unrealistic interest rate r_p , a realized nominal interest rate r_n , a growth rate of the deposits r_i , and a withdrawal rate r_w . Giving some restrictions on the rates r_p , r_i , and r_w , we prove some theorems to when the fund will collapse or be solvent. Two examples are given to illustrate the applicability of the main results.
alberto.cabada@usc.gal
Universidade de Santiago de Compostela, Spain
Title: Existence and multiplicity results for fourth order problems related to the theory of deformation beams
Abstract: In this talk we prove the and multiplicity of positive solutions for a fourth-order equation coupled to an integral perturbation of two-point boundary conditions. We apply the Krasnoselskii compression/expansion and Leggett-Williams fixed point theorems in suitable cones to show our multiplicity results. Finally, some particular cases are considered.
angelcid@uvigo.es
Universidade de Vigo, Spain
Title: Lyapunov stability for Brillouin–type equations
Co-author(s): Feng Wang; Shengjun Li; Miroslawa Zima
Abstract: Motivated by the Brillouin equation we deal with the existence and Lyapunov stability of periodic solutions for a more general kind of equations. Our approach is based on the third order approximation in combination with some location information obtained by the averaging method. We will show that our main results apply to some singular models not previously covered in the related literature.
z.elallali@ump.ma
Université Mohammed Premier, Morocco
Title: On a discrete elliptic problem with a weight
Co-author(s): Lingju Kong ; Mohamed Ousbika
Abstract: Using the variational approach and the critical point theory, we established several criteria for the existence of at least one nontrivial solution for a discrete elliptic boundary value problem with a weight $p(\cdot, \cdot)$ and depending on a real parameter $\lambda$.
guglielmo.feltrin@uniud.it
University of Udine, Italy
Title: Multiplicity of clines for systems of indefinite differential equations arising from a multilocus population genetics model
Co-author(s): Paolo Gidoni
Abstract: We investigate sufficient conditions for the presence of coexistence states for different genotypes in a diploid diallelic population with dominance distributed on a heterogeneous habitat, considering also the interaction between genes at multiple loci. In mathematical terms, this corresponds to the study of a Neumann boundary value problem associated with a system of parameter-dependent ODEs with indefinite coupling-weights. Using a topological degree approach, we prove high multiplicity of positive nontrivial solutions for large values of the parameters.
wfeng@trentu.ca
Trent University, Canada
Title: Uniqueness, multiplicity, upper and lower bounds of solutions for the perturbed Gelfand problem
Co-author(s): Shugui Kang; Youmin Lu
Abstract: We study the one-dimensional perturbed Gefand problem modelled as a two-point Boundary Value Problem associated with two parameters. Applying the theory for concave operators on partially ordered Banach spaces, we prove the existence of a unique solution when the activation energy parameter α≤4. As a general case, existence, upper and lower bounds of positive solutions are obtained using a new fixed point theorem on order intervals. For α>4, we give an estimation for a λ-interval such that there exist three positive solutions. Numerical examples are presented to illustrate the results including the case of three solutions.
c.goodrich@unsw.edu.au
UNSW Sydney, Australia
Title: A Topological Approach to Nonlocal Elliptic Partial Differential Equations on an Annulus
Abstract: By means of a nonstandard cone I will demonstrate the existence of at least one positive solution to nonlocal ODEs and nonlocal elliptic PDEs under Dirichlet-type boundary conditions. It will be shown that this approach improves results which rely on a more standard cone.
john-graef@utc.edu
University of Tennessee at Chattanooga, USA
Title: On solutions of a forced third order integro-differential equation
Abstract: The asymptotic behavior of the nonoscillatory solutions of a third order integro-differential equation with a forcing term and Laplacian is examined. The purpose is to determine whether the nonoscillatory solutions behave like certain non-linear functions. The proofs involve applications of Young’s, H ̈older’s, and Gronwall’s inequalities.
gennaro.infante@unical.it
University of Calabria, Italy
Title: Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem
Abstract: Motivated by recent interest on Kirchhoff-type equations, we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of elliptic functional differential equations. An example is presented to illustrate the theory.
lingju-kong@utc.edu
University of Tennessee at Chattanooga, USA
Title: Positive solutions for singular discrete Dirichlet problems
Co-author(s): Juhong Kuang
Abstract: By applying variational arguments and the lower and upper solution method, we obtain several criteria for the existence of positive solutions to a class of singular discrete Dirichlet problems with a parameter. Our results cover the cases when the nonlinear function in the equation is superlinear, asymptotically linear, and sublinear. We provide several examples to illustrate our results.
klan@ryerson.ca
Ryerson University, Canada
Title: Compactness of the first order Riemann-Liouville fractional integral operators
Abstract: This presentation is based on recent work on the first order Riemann-Liouville fractional integral operators. We first prove compactness of two linear Hammerstein integral operators with singularities, and then apply the result to give new proof that the first order Riemann-Liouville fractional integral operators with fraction $\alpha\in (0,1)$ map $L^{p}(0,1)$ to $C[0,1]$ and are compact for each $p\in \bigl(\frac{1}{1-\alpha},\infty\bigr]$.We show that the spectral radii of the first order Riemann-Liouville fractional integral operators are zero.
lilin420@gmail.com
Chongqing Technology and Business University, China
Title: A Nonlinear Klein–Gordon–Maxwell System in R2 Involving Singular and Vanishing Potentials
Co-author(s): Francisco S. B. Albuquerque
Abstract: In this paper, a nonlinear Klein–Gordon–Maxwell system in R2 and involving singular and vanishing potentials is considered. Under some mild assumptions on the potentials and nonlinearity, using variational methods and a Trudinger–Moser type inequality, we establish sufficient conditions for the existence of solution.
jlyons3@citadel.edu
The Citadel, USA
Title: An Application of the Layered Compression-Expansion Fixed Point Theorem to a Fractional Boundary Value Problem
Co-author(s): Sougata Dhar; Jeffrey T. Neugebauer
Abstract: In this talk, we show the existence of a positive solution of a fractional differential equation with a fractional boundary condition. We apply the recent Layered Compression Expansion Fixed Point Theorem, which requires the nonlinearity to be the sum of increasing and decreasing functions. The fact that the Green's function satisfies a positivity, increasing, and concavity-like condition will be integral to our analysis. An example is given.
Jeffrey.neugebauer@eku.edu
Eastern Kentucky University, USA
Title: First Extremal Point Comparison for a Fractional Boundary Value Problem with a Fractional Boundary Condition
Co-author: Johnny Henderson
Abstract: In this talk, we compare first extremal points of two fractional differential equations, each satisfying a fractional boundary condition. A weighted Banach space and sign properties of the Green's function play an important role in the analysis.
ricceri@dmi.unict.it
University of Catania, Italy
Title: Multiple periodic solutions of certain Lagrangian systems
Abstract: Ten years ago, Brezis and Mawhin showed that the global minima of a certain functional on the set of all vector L-Lipschitz functions u on [0,1], with u(0)=u(1), are solutions of a certain Lagrangian system. In my talk, I will present a multiplicty result for the global minima of that functional.
lwang5@kennesaw.edu
Kennesaw State University, USA
Title: Analysis of a general gene expression model with diffusion and delays
Co-author: Xiaoqin Wu
Abstract: In this research, we study a reaction-diffusion system of a general gene expression model with two time delays. The global existence of a unique strong solution and the existence of a global attractor are established. Using the sum of the two delays as the bifurcation parameter, critical values and conditions are derived so that the Hopf bifurcation at the unique equilibrium point may occur as the parameter crosses these critical values. For corresponding steady state solutions, the bounds for positive solutions are obtained using the Maximum Principle and the conditions for the system to have constant and non-constant solutions are investigated.
mwang23@kennesaw.edu
Kennesaw State University, USA
Title: A second order discrete boundary value problem with mixed periodic boundary conditions
Co-author(s): Lingju Kong
Abstract: In this talk, a second order discrete boundary value problem with a pair of mixed periodic boundary conditions is considered. Sufficient conditions on the existence of multiple solutions in a weak sense are obtained by using the critical point theory. Necessary conditions for a particular solution subject to pre-defined criteria are also investigated. Examples are given to illustrate the applications of the results as well.
pxiao4@kennesaw.edu
Kennesaw State University, USA
Title: Hypothalamus-pituitary-adrenal axis(HPA) modeling study
Abstract: The human stress response is controlled largely by the hypothalamic-pituitary-adrenal (HPA) axis. Models predicting the levels of the hormones involved are very often not analytically solvable because of nonlinear complexity. First, we will review the recent developments in this area, and then we propose an HPA model with the consideration of glucocorticoid receptor (GR) dynamics.
byang@kennesaw.edu
Kennesaw State University, USA
Title: Positive Solutions to a Boundary Value Problem for the Beam Equation
Abstract: We consider positive solutions for the boundary value problem of a nonlinear beam equation. Some upper and lower estimates for positive solutions are proved. Existence and nonexistence results for positive solutions of the problem are obtained.
bzhang@uncfsu.edu
Fayetteville State University, USA
Title: Fractional-Order Systems, Stability, and Iterative Method
Abstract: We study the stability properties of a system of fractional differential equations (FDEs) and give conditions to ensure that the zero solution is asymptotically stable by means of Gauss-Seidel type iterative method. The use of this method in differential equations of fractional-order is an area not yet widely investigated, although it proves to be very effective for equations of integer-order. In this project, we will refine the method to provide a new approach to the stability theory for FDEs and show that the solutions of FDEs with time-varying coefficients can still decay in time with an upper bound like t^(-α) as t→∞ , the property known only to exist in linear time-invariant fractional-order systems in the literature. We shall demonstrate that our iterative method converges much faster than the usual numerical procedures with sufficiently improved accuracy.