Document Type

Article

Publication Date

7-7-2014

Publication Title

Electronic Journal of Differential Equations

ISSN

1072-6691

Abstract

In this article, we study the existence of positive solutions for the p(x)-Laplacian Dirichlet problem −∆p(x)u = λf(x, u) in a bounded domain Ω ⊂ RN. The singular nonlinearity term f is allowed to be either f(x, s) → +∞, or f(x, s) → +∞ as s → 0+ for each x ∈ Ω. Our main results generalize the results in [15] from constant exponents to variable exponents. In particular, we give the asymptotic behavior of solutions of a simpler equation which is useful for finding supersolutions of differential equations with variable exponents, which is of independent interest.

Comments

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Mathematics Commons

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