Multiple solutions for a $p(x)$-Laplacian-like problem under Neumann boundary condition

K. Kefi

doi:10.3842/umzh.v76i8.7575

K. Kefi Faculty of Computing and Information Technology, Northern Border University, Rafha, Kingdom of Saudi Arabia

DOI: https://doi.org/10.3842/umzh.v76i8.7575

Keywords: $p(x)$-Laplacian like problem, critical theorem, generalized Sobolev space, variable exponent

Abstract

UDC 517.9

We prove the existence of at least three weak solutions for a class of $p(x)$-Laplacian-like problems with Neumann boundary conditions by using a critical theorem of Bonanno and Marano [Appl. Anal., 89, 1–10 (2010)].

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