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

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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.

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Funding

Supported by the National Natural Science Foundation of China (61803236), Natural Science Foundation of Shandong Province (ZR2018MA022).

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Authors and Affiliations

  1. School of Mathematics Statistics, Shandong Normal University, Jinan, 250358, People’s Republic of China

    Huiqin Lu, Xinmin Qu & Jianing Wang

Authors
  1. Huiqin Lu
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  2. Xinmin Qu
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  3. Jianing Wang
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Corresponding author

Correspondence to Huiqin Lu.

Additional information

This article is part of the topical collection dedicated to Prof. Dajun Guo for his 85th birthday, edited by Yihong Du, Zhaoli Liu, Xingbin Pan, and Zhitao Zhang.

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Lu, H., Qu, X. & Wang, J. Sign-changing and constant-sign solutions for elliptic problems involving nonlocal integro-differential operators. SN Partial Differ. Equ. Appl. 1, 33 (2020). https://doi.org/10.1007/s42985-020-00028-w

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