Sign-changing and constant-sign solutions for elliptic problems involving nonlocal integro-differential operators

Huiqin Lu (), Xinmin Qu and Jianing Wang
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Huiqin Lu: Shandong Normal University
Xinmin Qu: Shandong Normal University
Jianing Wang: Shandong Normal University

Partial Differential Equations and Applications, 2020, vol. 1, issue 5, 1-17

Abstract: Abstract This work is devoted to study the existence of sign-changing and constant-sign solutions for nonlinear elliptic problems driven by nonlocal integro-differential operators with subcritical nonlinearity which is not locally Lipschitz continuous and there is no (AR) condition and no any monotony properties. By using some variants of the Mountain Pass Lemma, we show the existence of a positive solution, a negative solution and a sign-changing solution.

Keywords: Nonlocal operators; Sign-changing solution; Constant-sign solution; Mountain Pass Lemma; Variational methods; 35J65; 47J05; 47J30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00028-w

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