# American Institute of Mathematical Sciences

June  2021, 14(6): 1837-1855. doi: 10.3934/dcdss.2021007

## Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero

 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

* Corresponding author: Jiabao Su

Received  August 2020 Revised  November 2020 Published  June 2021 Early access  January 2021

Fund Project: Supported by NSFC(12001382, 11771302) and KZ202010028048

In this paper we obtain the existence of nontrivial solutions for the fractional Laplacian equations with the nonlinearity may fail to have asymptotic limits at zero and at infinity. We make use of a combination of homotopy invariance of critical groups and the topological version of linking methods.

Citation: Yutong Chen, Jiabao Su. Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero. Discrete & Continuous Dynamical Systems - S, 2021, 14 (6) : 1837-1855. doi: 10.3934/dcdss.2021007
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