Existence and uniqueness results for discrete second-order periodic boundary value problems
Ferhan M. Atıcı,Alberto Cabada +1 more
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In this paper, the existence and uniqueness results for solutions of second-order nonlinear difference equations on a finite discrete segment with periodic boundary conditions were proved based on the notion of upper and lower solutions.Abstract:
We prove existence and uniqueness results for solutions of second-order nonlinear difference equations on a finite discrete segment with periodic boundary conditions. The results are based on the notion of upper and lower solutions.read more
Citations
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Existence and multiple solutions for a second-order difference boundary value problem via critical point theory
Haihua Liang,Peixuan Weng +1 more
TL;DR: In this article, the critical point theory is employed to establish existence and multiple solutions for a second-order difference boundary value problem, which is a special case of the boundary value maximization problem.
Journal ArticleDOI
On variational methods for periodic discrete problems
TL;DR: In this article, the existence results for a general 2n-th order discrete boundary value problem subjected to periodic conditions were proved for the first-order case, and the existence and uniqueness theorems were improved by including non-continuous right-hand sides, higher-order problems and non-invertible difference operators.
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Solutions for discrete p-Laplacian periodic boundary value problems via critical point theory
TL;DR: In this article, a class of discrete p-Laplacian periodic boundary value problems was studied by using critical point theory and some results were obtained for the existence of two positive solutions, three solutions and multiple pairs of solutions when the parameter lies in some suitable infinite or finite interval.
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Existence of solutions to nonlinear first-order PBVPs on time scales
TL;DR: In this article, the first-order periodic boundary value problem was studied and the existence criteria of at least one solution were established by using novel inequalities and the well-known Schaefer fixed point theorem.
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Nontrivial periodic solutions for asymptotically linear resonant difference problem
TL;DR: In this article, the existence of nontrivial periodic solution for second order asymptotically linear difference equation at resonance is obtained based on combining the minimax methods and the Morse theory, especially the observation on the critical groups.
References
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Book
Difference Equations: An Introduction with Applications
Walter G. Kelley,Allan Peterson +1 more
TL;DR: The Difference Calculus of Variations as discussed by the authors is a generalization of the Difference calculus of Difference Equations (DCE) of the calculus of Variants (CDE) of Difference Functions.
Book
Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations
Seppo Heikkilä,V. Lakshmikantham +1 more
TL;DR: In this paper, First Order Differential Equations (FDE) and Second Order Differentially Equations in Banach Spaces (SODE) are used to solve the problem.