Existence and multiplicity of solutions for $p(x)$-Laplacian problem with Steklov boundary condition

Abstract

We study the existence and multiplicity of weak solutions for an elliptic problem involving $p(x)$ p ( x ) -Laplacian operator under Steklov boundary condition. The approach is based on variational methods.

Multiple Solutions for a Class of Biharmonic Nonlocal Elliptic Systems

“…Theorem 1.1 ensures that for each ∈ Λ r, , the functional I admits at least three critical points in X that are weak solutions of the problem (1.1). ◻ Remark 3.1 An interesting problem is to probe the existence and multiplicity of solutions of this system under the Steklov boundary conditions [8] or in the Heisenberg Sobolev spaces and Orlicz Sobolev spaces. Interested reader can see details of these spaces in [5,6,[12][13][14][15][16]20] and references therein.…”

Existence of Entropy Solution for a Nonlinear Parabolic Problem in Weighted Sobolev Space via Optimization Method

“…)-Laplacian problem. Also, in [13], Khaleghi and Razani investigated the existence and multiplicity of weak solution for an elliptic problem involving p(. )-Laplacian operator under Steklov boundary condition, the approach was based on variational methods.…”

Solutions to a $$(p_1, \ldots ,p_n)$$-Laplacian Problem with Hardy Potentials

“…positive in an open set. In 2019, Behboudi et al [2] verified the existence of two weak solutions for the following problem where 2 ≤ q < p < N (one can see [9,10,12,13,17,[20][21][22][23][24][25]33] and references therein for the importance of study of these kinds of problems).…”