Electron. J. Diff. Equ., Vol. 2015 (2015), No. 109, pp. 1-12.

A sign-changing solution for nonlinear problems involving the fractional Laplacian

Kaimin Teng, Kun Wang, Ruimeng Wang

Abstract:
In this article, we establish the existence of a least energy sign-changing solution for nonlinear problems involving the fractional Laplacian. Our main tool is constrained minimization in a closed subset containing all the sign-changing solutions of the equation.

Submitted March 12, 2015. Published April 21, 2015.
Math Subject Classifications: 35B38, 35D05, 35J20.
Key Words: Sign-changing solutions; fractional Laplacian; minimization; Nehari manifold

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Kaimin Teng
Department of Mathematics, Taiyuan University of Technology
Taiyuan, Shanxi 030024, China
email: tengkaimin2013@163.com
  Kun Wang
Department of Mathematics, Taiyuan University of Technology
Taiyuan, Shanxi 030024, China
email: 1090417245@qq.com
  Ruimeng Wang
Department of Mathematics, Taiyuan University of Technology
Taiyuan, Shanxi 030024, China
email: 1042583643@qq.com

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