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