一类N-双调和方程多解的存在性

The Existence of Solutions for a Class of N-biharmonic Equation

研究一类N双调和方程△N^2u-△Nu＋V（x）｜u｜^N-2u=f（x,u）,x∈R^N 其中f（x，u）=λg（x）｜u｜^p-2u＋h（u），1〈P〈N，λ≥0是参数，权函数V（x），9（x），h（u）满足一定的条件．运用对称山路定理和Schwarz对称化方证明了方程存在无穷多个弱解．

In this paper, we consider a class of N-biharmonic function： △N^2u-△Nu＋V（x）｜u｜^N-2u=f（x,u）,x∈R^N where f（x, u） = λg（x）｜u｜^P-2u＋h（u）, 1 〈 p 〈 N, A ≥ 0, The weight functions V（x）,g（x）, h（u） satisfy some suitable conditions. Applying symmetric Mountain Pass Theorem and Schwaxz symmetrization method, we prove the problem had infinitely many solutions.