Electron. J. Differential Equations, Vol. 2017 (2017), No. 18, pp. 1-11.

Multiple solutions to fractional equations without the Ambrosetti-Rabinowitz condition

Ruichang Pei, Jihui Zhang, Caochuan Ma

Abstract:
In this article we study a class of fractional Laplace equations which do not satisfy the Ambrosetti-Rabinowitz condition (AR-condition). We establish the existence of three nontrivial solutions and of multiple sign changing solutions by using Morse theory.

Submitted April 30, 2016. Published January 14, 2017.
Math Subject Classifications: 35J60, 35J91, 58E05.
Key Words: Fractional Laplacian; Morse theory; sign changing solution; improved subcritical polynomial growth.

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Ruichang Pei
School of Mathematics and Statistics
Tianshui Normal University
Tianshui 741001, China
email: prc211@163.com
Jihui Zhang
Institute of Mathematics
School of Mathematics and Computer Sciences
Nanjing, Normal University
Nanjing 210097, China
email: zhangjihui@njnu.edu.cn
  Caochuan Ma
School of Mathematics and Statistics
Tianshui Normal University
Tianshui 741001, China
email: macaoch@163.com

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