Using variational methods and critical point theory, the existence of infinitely many solutions for perturbed nonlinear difference equations with discrete Dirichlet boundary conditions is ensured.
Abstract. Using critical point theory, we study the existence of at least three solutions for perturbed nonlinear difference equations with discrete boundary-value condition depending on two positive parameters.
Abstract. The existence of a non-trivial solution for a discrete non-linear Dirichlet problem involving p -Laplacian is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Bonanno.Mathematics subject classification (2010): 39A10, 34B15.
Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p.k/-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Riccerilocal minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.
Abstract. In the present paper, by using variational method, the existence of non-trivial solutions to an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary condition is investigated. The main technical tools applied here are the two local minimum theorems for differentiable functionals given by Bonanno.
IntroductionThe main goal of the present paper is to establish the existence of non-trivial solution for the following discrete anisotropic problem We want to remark that problem (1.1) is the discrete variant of the variable exponent anisotropic problem2) where Ω ⊂ R N , N ≥ 3 is a bounded domain with smooth boundary, f ∈ C(Ω×R, R) is given function that satisfy certain properties and p i (x), w i (x) ≥ 1 and q(x) ≥ 1 are continuous functions on Ω with 2 ≤ p i (x) for each x ∈ Ω and every i ∈ 2000 Mathematics Subject Classification. 39F20, 34B15.
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