没有Landesman-Lazer型条件的拟线性强振动方程之无穷多解  

Infinitely Many Solutions for the Resonant Quasi-linear Equation Without Landesman-Lazer Conditions

作　　者：饶若峰[1] 王雄瑞[1] 

机构地区：[1]四川宜宾学院数学系,四川宜宾644007

出　　处：《数学物理学报（A辑）》2012年第4期744-752,共9页Acta Mathematica Scientia

基　　金：四川省教育厅(青年)自然科学基金(08ZB008);宜宾学院重点项目(2011Z04)资助

摘　　要：椭圆型振动方程往往需要一个所谓的Landesman-Lazer型条件假设.但该文充分利用第一特征函数的性质以及亏格技巧在没有Landesman-Lazer型条件假设的情况下给出了强振动方程-Δ_pu=λ_1|u|^(p-2)u+g(x,u)无穷多解的存在性结论,将一些最近结论从几个有限解的存在性推广到无穷多解的存在性结果.The famous Landesman-Lazer conditions is used to be applied in solving the existent solution for elliptic resonant equations.In this paper,the author is by using the property of the space of the first eigenfunctions and the technique of genus to give an existence theorem for infinitely many solutions of the strong resonant equation -Δpu =λ1｜u｜～（p-2）＋ g（x,u） without any Landesman-Lazer conditions,which extends some recent results from single or several solutions to infinitely many solutions.

关 键 词：P-LAPLACIAN算子 形变引理 Palais—Smale条件 

分 类 号：O175.25[理学—数学]