数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1296-1310.doi: 10.1016/S0252-9602(18)30815-4

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THREE NONTRIVIAL SOLUTIONS FOR A NONLINEAR ANISOTROPIC NONLOCAL EQUATION

Amin ESFAHANI   

  1. School of Mathematics and Computer Science, Damghan University, 36715-364 Damghan, Iran
  • 收稿日期:2016-09-02 修回日期:2017-11-11 出版日期:2018-08-25 发布日期:2018-08-25
  • 作者简介:Amin ESFAHANI,E-mail:esfahani@du.ac.ir,amin@impa.br

THREE NONTRIVIAL SOLUTIONS FOR A NONLINEAR ANISOTROPIC NONLOCAL EQUATION

Amin ESFAHANI   

  1. School of Mathematics and Computer Science, Damghan University, 36715-364 Damghan, Iran
  • Received:2016-09-02 Revised:2017-11-11 Online:2018-08-25 Published:2018-08-25

摘要:

In this article, we establish the existence of a sign-changing solution and two sign-constant solutions for nonlinear nonlocal problem involving the BO-ZK operator on bounded domain. Our main tool is constrained minimization on appropriate Nehari manifolds.

关键词: sign-constant and nodal solutions, BO-ZK operator, variational method

Abstract:

In this article, we establish the existence of a sign-changing solution and two sign-constant solutions for nonlinear nonlocal problem involving the BO-ZK operator on bounded domain. Our main tool is constrained minimization on appropriate Nehari manifolds.

Key words: sign-constant and nodal solutions, BO-ZK operator, variational method