Jung-Hyun Bae, Yun-Ho Kim
In this article, we establish the existence of three weak solutions for elliptic equations associated to the fractional Laplacian
where is an open bounded subset in with Lipschitz boundary, is a real parameter, 0<s<1, N>2s, and 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 for which the problem above with discontinuous nonlinearities admits at least three nontrivial weak solutions by applying two recent three-critical-points theorems.
Submitted April 26, 2018. Published January 30, 2019.
Math Subject Classifications: 58E30, 49J52, 58E05.
Key Words: Fractional Laplacian; three-critical-points theorem; multiple solutions.
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| Jung-Hyun Bae |
Department of Mathematics
Suwon 16419, Korea
| Yun-Ho Kim |
Department of Mathematics Education
Seoul 03016, Korea
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