Ground state and mountain pass solutions for discrete p ( ⋅ ) -Laplacian

Mountain pass and linking type sign-changing solutions for nonlinear problems involving the fractional Laplacian

where ⊂Rn (n≥ 2) is a bounded smooth domain, s ∈ (0, 1), (– )s denotes the fractional Laplacian, λ is a real parameter, the nonlinear term f satisfies superlinear and subcritical growth conditions at zero and at infinity. When λ≤ 0, we prove the existence of a positive solution, a negative solution and a sign-changing solution by combing minimax method with invariant sets of descending flow. Wh...

Existence of solutions for p-Laplacian discrete equations

This work is devoted to the study of the existence of at least one (non-zero) solution to a problem involving the discrete p-Laplacian. As a special case, we derive an existence theorem for a second-order discrete problem, depending on a positive real parameter a, whose prototype is given by Duðk 1Þ 1⁄4 af ðk;uðkÞÞ; 8k 2 Z1⁄21; T ; uð0Þ 1⁄4 uðT þ 1Þ 1⁄4 0: ( Our approach is based on variational...

Homoclinic solutions for second order discrete p-Laplacian systems

* Correspondence: hxfcsu@sina. com Department of Mathematics and Computer Science Jishou University, Jishou, Hunan 416000, P. R. China Full list of author information is available at the end of the article Abstract Some new existence theorems for homoclinic solutions are obtained for a class of second-order discrete p-Laplacian systems by critical point theory, a homoclinic orbit is obtained as...

On the dependence on parameters for mountain pass solutions of second order discrete BVP's

We investigate the continuous dependence on parameters for the mountain pass solutions of second order discrete equations with p-Laplacian and Dirichlet type boundary conditions. We show that assumptions leading to the existence of nontrivial solutions lead also to its continuous dependence on parameters. We investigate also the uniqueness of solutions. 2012 Elsevier Inc. All rights reserved.

Existence of Periodic Solutions for a Class of Asymptotically p-Linear Discrete Systems Involving p-Laplacian