Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 535-544.

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Sufficient and Necessary Condition for the Existence of Positive Entire Solutions of a Nonlinear Biharmonic Equations on ${{\mathbb{R}}^{N}}$

Xiaohang Ou()   

  1. Shunde Polytechnic, Guangdong Foshan 528333
  • Received:2018-02-13 Online:2019-06-26 Published:2019-06-27


The aim of this paper is to study the nonlinear biharmonic equations of the following form $\triangle^2u=f(|x|, u, |\nabla u|)(x\in \mathbb{R} ^N, N>2)$. The Sufficient and necessary condition for the existence of positive entire solutions is proved, and some properties of the solutions are obtained.

Key words: Nonlinear biharmonic equation, Positive entire solution, Close convex subset, Equicontinuity, Fixed point theorem

CLC Number: 

  • O175.25