Nontrivial solutions for a fourth-order elliptic equation of Kirchhoff type via Galerkin method



In this paper we study the existence of nontrivial solutions of the nonlocal elliptic problem
$$\begin{aligned} \left\{ \begin{array}{lcr} \Delta ^2 u-(a+b\int _\Omega |\nabla u|^2\mathrm{d}x)\Delta u+u=(\int _\Omega g(x,u)\mathrm{d}x)^\gamma f(x,u),\;in\;\Omega ,\\ u=\Delta u=0,\;\;on\;\;\partial \Omega \end{array}\right. \end{aligned}$$
via Galerkin method, where \(\Omega \subset \mathbb {R}^N (N\ge 5)\) is a smooth bounded domain.


Nonlocal elliptic problems biharmonic operator Galerkin method 

Mathematics Subject Classification

Primary 35J58 35J65 



The authors would like to thank the referees for the helpful suggestions.


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Authors and Affiliations

  1. 1.Depatment of Mathematics, College of ScienceHohai UniversityNanjingPeople’s Republic of China
  2. 2.College of ScienceChina pharmaceutical UniversityNanjingPeople’s Republic of China

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