R^N中带周期位势的超线性p-Laplacian方程的无穷多解  

Infinitely Many Solutions of Superlinear p-Laplacian Equation with Periodic Potentials in R^N

作　　者：张文丽[1] 

机构地区：[1]长治学院数学系,长治046011

出　　处：《应用泛函分析学报》2012年第2期166-171,共6页Acta Analysis Functionalis Applicata

摘　　要：在非线性项f是关于u的奇函数,势函数是有界的周期函数且下界是正的,Sobolev嵌入缺乏了紧性和f不再满足(AR)条件下,运用临界点理论中的喷泉定理和集中紧性原则证明了R^N中具有周期势函数的一类超线性p-Laplacian方程存在无穷多非平凡解。Under these assumptions that the nonlinearity is odd about u,potentials is bounded and periodic and the lower is positive,Sobolev implant is short of tightness and f is no longer satisfy （AR） condition,by using Fountain theorem and concentration-compactness principle,we study the existence of infinitely many solutions for a superlinear p-Laplacian equation in R^N with periodic potentials.

关 键 词：集中紧性原理 (C)条件 喷泉定理 

分 类 号：O175.25[理学—数学]