Jung-Hyun Bae, Yun-Ho Kim
Abstract:
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 Sungkyunkwan University Suwon 16419, Korea email: hoi1000sa@skku.edu |
Yun-Ho Kim Department of Mathematics Education Sangmyung University Seoul 03016, Korea email: kyh1213@smu.ac.kr |
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