Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

Bulletin of the Australian Mathematical Society

Abstract

We consider the Dirichlet problem for p(x)-Laplacian equations of the form -Δp(x)u + b(x)|u| p(x)-2 u = f(x, u), u ∈ W1,p(x) 0 (ω). The odd nonlinearity f(x, u) is p(x)-sublinear at u = 0 but the related limit need not be uniform for x ∈ ω. Except being subcritical, no additional assumption is imposed on f(x, u) for |u| large. By applying Clark s theorem and a truncation method, we obtain a sequence of solutions with negative energy and approaching the zero function u = 0. © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

First Page

346

DOI

10.1017/S0004972723001405

Publication Date

2024

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