Multiple solutions for discontinuous elliptic problems involving the fractional Laplacian
Files
Date
2019-01-30
Authors
Bae, Jung-Hyun
Kim, Yun-Ho
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we establish the existence of three weak solutions for elliptic equations associated to the fractional Laplacian
(-∆)su = λƒ(x, u) in Ω,
u = 0 on ℝN \ Ω,
where Ω is an open bounded subset in ℝN with Lipschitz boundary, λ is a real parameter, 0 < s < 1, N > 2s, and ƒ : Ω x ℝ → ℝ is measurable with respect to each variable separately. The main purpose of this paper is concretely to provide an estimate of the positive interval of the parameters λ for which the problem above with discontinuous nonlinearities admits at least three nontrivial weak solutions by applying two recent three-critical-points theorems.
Description
Keywords
Fractional Laplacian, Three-critical-points theorem, Multiple solutions
Citation
Bae, J. H., & Kim, Y. H. (2019). Multiple solutions for discontinuous elliptic problems involving the fractional Laplacian. <i>Electronic Journal of Differential Equations, 2019</i>(18), pp. 1-16.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.