具有非对称项p-Laplace方程的无穷多解  

Infinitely Many Solutions of p-Laplacian Equations with a Nonsymmetric Term

作　　者：耿堤[1] 刘迪生[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《吉首大学学报（自然科学版）》2008年第5期1-4,共4页Journal of Jishou University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10371045);广东省自然科学基金资助项目(7005795)

摘　　要：讨论了有界区域上一类具有非对称扰动项的p-Laplace方程.利用对应的Laplace方程大Morse指标,给出了该问题变分泛函极小极大值序列的一个下界估计,这个估计在一定范围内优于已有的结论.进而得到了无穷多个弱解的存在性.A class of p-Laplace equation with a nonsymmetric term on a bounded domain is studied. By using the large Morse index of the corresponding Laplace equation, we give a growth estimate about the series of min-max values of associated functional for the problem. The estimate is better than the given result in some range. It is shown that the problem possesses infinitely many weak solutions.

关 键 词：P-LAPLACE算子 大Morse指标 非奇性扰动 无穷多解 

分 类 号：O175.25[理学—数学]