Electron. J. Differential Equations, Vol. 2017 (2017), No. 234, pp. 1-26.

Existence and multiplicity of solutions for nonlinear equations involving the square root of the Laplacian

Yutong Chen, Jiabao Su, Huanhong Yan

Abstract:
This paper deals with the existence and multiplicity results for fractional problem involving the square root of the Laplacian $A_{1/2}$ in a bounded domain with zero Dirichlet boundary conditions by Morse theory and critical groups for a $C^{1}$ functional at both isolated critical points and infinity.

Submitted June 21, 2017. Published September 29, 2017
Math Subject Classifications: 35J10, 35J65 58E05.
Key Words: Fractional Laplacian; variational methods; critical group; Morse theory.

Show me the PDF file (364 KB), TEX file for this article.

Yutong Chen
School of Mathematical Sciences
Capital Normal University
Beijing 100048, China
email: chenyutong@cnu.edu.cn
Jiabao Su
School of Mathematical Sciences
Capital Normal University
Beijing 100048, China
email: sujb@cun.edu.cn
Huanhong Yan
School of Mathematical Sciences
Capital Normal University
Beijing 100048, China
email: 1464938716@qq.com

Return to the EJDE web page