摘要
讨论了带非负扰动并具有第二类边值的临界非齐次多重调和方程的多解存在性和非存在性 .首先将方程化成与之等价的方程组 ,当λ≥ 0时 ,利用方程组的拟单增性和单个方程的极值原理求得方程的第一个正解 ,当λ <0时 ,利用Schauder不动点定理求得方程的第一个正解 ;再用山路引理得出方程在一定条件下存在第二个正解 ;最后 ,用推广的Po hozave恒等式讨论了当λ <0 ,N≥ 6m时方程第二个解的非存在性 .参 10 .
This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with the second boundary and with a non-negative perturbation.First of all,the polyharmonic equation be become a group of elliptic equations,if λ≥0 ,its first solution is proved via the quasi-monotone growth of the group of elliptic equations and the maximum principle of elliptic equation,if λ<0, its first solution is obtained by using Schauder theorem.And its second solution is got via mountain pass limma in a certain condition;furthermore,as λ<0,N≥6m ,nonexistence of its second solution is obtained by employing a improving Pohozaev's identity.10refs.
出处
《湘潭矿业学院学报》
2001年第2期82-85,共4页
Journal of Xiangtan Mining Institute
基金
国家自然科学基金项目 (1 961 0 34)
