Solutions for p(x)-Laplace equations with critical frequency

Date

2018-01-19

Authors

Zhang, Xia
Zhang, Chao
Gao, Huimin

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article concerns the p(x)-Laplace equations with critical frequency -div(|∇u|p(x)-2∇u) + V(x)|u|p(x)-2u = ƒ(x, u) in ℝN, where 1 < p- ≤ p(x) ≤ p+ < N. We study this equation with the potentials being zero. By using variational method, we obtain the existence of nonnegative solutions. Moreover, if ƒ(x, t) is odd in t, for any m ∈ ℕ we derive m pairs of nontrivial solutions.

Description

Keywords

Variable exponent space, p(x)-Laplace, Critical frequency, Weak solution

Citation

Zhang, X., Zhang, C., & Gao, H. (2018). Solutions for p(x)-Laplace equations with critical frequency. <i>Electronic Journal of Differential Equations, 2018</i>(31), pp. 1-20.

Rights

Attribution 4.0 International

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