具有不定位势的渐近线性p-Laplacian Dirichlet问题
Asymptotically linear p-Laplacian Dirichlet problem with indefinite weights
摘要
利用山路引理及极小作用原理,证明了当非线性项在无穷远处满足一定的渐近线性条件时,具有不定位势的渐近线性p-Laplacian Dirichlet问题,存在非平凡解.
By using mountain pass and the least action theorems, the existience of nontrivial solution is obtained for a class of asymptotically linear p-Laplacian Dirichlet problem with indefinite weights.
出处
《纯粹数学与应用数学》
CSCD
2012年第4期501-506,共6页
Pure and Applied Mathematics
基金
天水师范学院中青年教师科研资助项目(TSA0937)
参考文献11
-
1Amborosetti A, Rabinowitz P H. Variational methods in critical theory and application[J]. Punct. Anal” 1973,14:349-381.
-
2Benci V, Rabinowitz P H. Critical point theorems for indefinite functional[J], Invent. Math., 1979,52:241-273.
-
3Smarandache F. Critical Point Theory and Applications[M].上海:上海科学技术出版社,1986.
-
4Cuesta M. Eigenvalue problems for the p-Laplacian with indefinite weight [J], Electronic Journal of Differential Equations, 2001,33:1-9.
-
5.Xuan B J. Existence results for a super linear p-Laplacian equation with indefinite weights [J]. Nonlinear Analysis, 2003,54:949-958.
-
6Sun J P, Li W T. Multiple positive solutions to second-order Neumann boundary value problems [J]. Appl. Math. Comput., 2003,146:187-194.
-
7Gossez J P, Leadi L. Asymmetric elliptic problems in IRn [J]. Electronic Journal of Differential Equations, 2006,14:207-222.
-
8Shao Z Q, Hong J X. The eigenvalue problem for the Laplacian equations[J]. Acta. Mathematica Scientia, 2007,02:329-337.
-
9Ariasa M, Camposea J, Cuestab M. An asymmetric Neumann problem with weights[J]. Nonlinear Analysis, 2008,25:267-280.
-
10Cuesta M, Quoirin H R. A weighted eigenvalue problem for the p-Laplacian plus a potential [J]. Nonlinear Differ. Equ. Appl.,2009,16:469-491.