Sequences of Weak Solutions for Non-Local Elliptic Problems with Dirichlet Boundary Condition

Abstract

In this paper the existence of infinitely many solutions for a class of Kirchhoff-type problems involving the p-Laplacian, with p > 1, is established. By using variational methods, we determine unbounded real intervals of parameters such that the problems treated admit either an unbounded sequence of weak solutions, provided that the nonlinearity has a suitable behaviour at ∞, or a pairwise distinct sequence of weak solutions that strongly converges to 0 if a similar behaviour occurs at 0. Some comparisons with several results in the literature are pointed out. The last part of the work is devoted to the autonomous elliptic Dirichlet problem.

A Variational Approach to Perturbed Discrete Anisotropic Equations

“…Then, one has the following: We refer the reader to the paper [41][42][43][44][45][46][47] in which Theorem 1 was successfully employed to ensure the existence of infinitely many solutions for boundary value problems.…”

Existence results for a Kirchhoff-type problem with singularity

“…In recent years, the study of elliptic problems involving Kirchhoff type operators have been studied in many works, we refer to [1, 3, 5-7, 16-18, 20, 22]. For instance, in [17], Molica Bisci and Pizzimenti considered the following problem…”

Existence and Multiplicity of Positive Solutions for Kirchhoff-Type Equations with the Critical Sobolev Exponent

“…problem (4) received much attention, and we refer the readers to [8][9][10][11][12][13][14][15] for more details and the references therein. More precisely, Bisci and Pizzimenti [13] studied the existence of infinitely many solutions for a class of Kirchhofftype problems involving the p-Laplacian by using variational methods. In [15], Bisci considered the existence of (weak) solutions for some Kirchhoff-type problems on a geodesic ball of the hyperbolic space and the main technical approach is based on variational and topological methods.…”