带有Neumann边界的类p-Laplace方程无穷多解存在性

下载PDF

导出

摘要讨论中有界光滑区域上的一类带有Neumann边界的类p-Laplace方程的无穷多解问题,其中,非线性项不必具有奇对称性,用寻找局部极小值的方法得到两列非负弱解,并且当非线性项在零点（无穷远点）振荡时,两列解按范数趋于零（趋于正无穷）,同时对应的能量函数趋于零（趋于负无穷）。

作者郭慧敏邵泽军丁茂震

机构地区北京化工大学北方学院基础课部

出处《科技与生活》 2010年第11期158-159,154,共3页

关键词类p-Laplace算子 NEUMANN边界局部极小值无穷多解

参考文献7

1郭慧敏,耿堤.类p-双调和方程Dirichlet问题无穷多解的存在性[J].华南师范大学学报（自然科学版）,2009,41(1):18-21. 被引量：3
2KRISTALY A,MOROSANU G,TERSIAN S.Quasilinear elliptic problems in Rn involving oscillatory nonlinearities[J].J.Diff.Eqau,20O7,235:366-375.
3AMBROSETTI A,RABINOWITZ P H.Dual variational methods in critical point theory and applications[J].J.Func.Anal,1973,14:349-381.
4KAJIKIYA R.A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations[J].J.Func.Anal,2005,225:352-370.
5刘轼波,李树杰.一类超线性椭圆方程的无穷多解[J].数学学报（中文版）,2003,46(4):625-630. 被引量：22
6耿堤.含极限次临界增长项p-Laplace方程的无穷多解[J].应用数学和力学,2007,28(10):1223-1231. 被引量：6
7CAMMAROTO F,CHINNI A,BELLA B D.Infinitely many solutions for the Dirichlet problem involving the p-Laplace[J].Nonl.Anal.2005,61:41-49.

1AMBROSETTI A, RABINOWITZ P H. Dual variational methods in critical point theory and applications [ J ]. J Func Anal, 1973,14:349 - 381.
2KAJIKIYA R. A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations [ J ]. J Func Anal,2005,225 : 352 - 370.
3OMARI P F. Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential[J]. Comm Part Diff Equa,1996,21:721 -733.
4OMARI P,ZANOLIN F. An elliptic problem with arbitra- rily small positive solutions [ J ]. Nonl Diff Equa, 2000,5 : 301 - 308.
5CAMMAROTO F, CHINNI A, BELLA B D. Infinitely many solutions for the Dirichlet problem involving the p - Laplace[ J]. Nonl Anal,2005,61 : 41 - 49.
6RICCERI B. A general variational principle and some of its applications [ J ]. J Comp Appl Math,2000,113 : 401 - 410.
7Ambrosetti A., Rabinowitz P. H., Dual variational methods in critical point theory and applications, J. Funct.Anal.. 1973. 14: 349-381.
8Zou W. M., Variant fountain theorems and their applications, Mannsc. Math.. 2001. 104: 343-358.
9Li G. B., Zhou H. S., Asymptotically linear Dirichlet problem for the p-Laplacian, Nonl. Anal. TMA, 2001,45: 1043-1055.
10Stuart C. A., Zhou H. S., A variational problem related to self-trapping of an electromagnetic field, Math.Methods in the Applied Sciences. 1996. 19: 1397-1407.

科技与生活

2010年第11期

内容加载中请稍等...