一类半线性椭圆边值问题的多解性
Multiple solutions to a semilinear elliptic boundary value problem
摘要
利用临界点以及拓扑度理论讨论了一类半线性椭圆型方程边值问题的多解性,得到了适当条件下存在3个解的结论.
Multiple solutions to a semilinear elliptic boundary value problem were discussed using the critical point and the theories of topological degree. It was concluded that there are three solutions under suitable conditions.
出处
《河海大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第4期487-491,共5页
Journal of Hohai University(Natural Sciences)
参考文献10
-
1SU Jia-bao, ZHAO Lei-ga. An elliptic resonance problem with multiple solutions[J]. Journal of Mathematical Analysis and Applications, 2006.319: 604-616.
-
2LANDESMAN E, ROBINSON S, RUMBOS A. Multiple solutions of semilinear elliptic problems at resonance[ J]. Nonlinear Analysis, 1995,24:1049-1059.
-
3AHMAD S. Multiple nontrivial solutions of resonant and nonresonant asymptotically linear problems [J]. Proceedings of the American Mathematical Society, 1986,96: 405-409.
-
4AMBROSETTI A. Equadiff 82: Proceedings of the International Conference Held in Wurzburg, FRG, August 23-28, 1982[ C]. Berlin: Springer, 1983.
-
5HOFER H. A note on the topological degree at a critical point of mountain pass type [ J ]. Proceedings of the American Mathematical Society, 1984,90: 309-315.
-
6GARZA G L, RUMBOS A. Multiple solutions for resonant semilinear elliptic problems in R^N[J]. Journal of Mathematical Analysis and Applications, 2005,305 : 367-379.
-
7RUDIN W. Functional analysis[ M]. Columbus: McGraw-Hill Companies, 1991.
-
8MAWHIN J, WILLEM M. Critical point theory and hamitonian systems[ M]. New York: Springer-Verlag, 1989.
-
9RUMBOS A. A semilinear elliptic boundary value problem at resonance where the nonlinearity may grow linearly[J]. Nonlinear Analysis, 1991,16:1159-1168.
-
10IAIA J A. A priori estimates for a similinear elliptic PDE[J]. Nonlinear Analysis, 1995,24:1039-1048.
-
1宋树枝.两点边值拟线性椭圆方程共振问题的注记[J].重庆工商大学学报（自然科学版）,2006,23(3):234-239. 被引量：1
-
2赵家辉,张申贵.一类椭圆方程Neumann边值问题解的存在性[J].甘肃科学学报,2006,18(3):10-12. 被引量：3
-
3赵青,贾高.一类高阶拟线性椭圆方程共振问题的可解性[J].上海理工大学学报,2009,31(1):1-5. 被引量：2
-
4宋树枝,唐春雷.p-Lapacian方程关于Fuík谱共振问题解的存在性[J].西南大学学报（自然科学版）,2016,38(10):55-61.
-
5饶若峰,黄家琳,张玲.拟线性强振动方程解的存在性[J].大学数学,2009,25(2):114-119.
-
6陆晓鸣.一类半线性椭圆边值问题的多解结果[J].兰州大学学报（自然科学版）,1989,25(2):1-6.
-
7沈铨,丁睿.一类半线性椭圆边值问题的无网格方法[J].苏州大学学报（自然科学版）,2006,22(4):14-17.
-
8安幼山,胡建勋.一类带跨越多重本征值非线性项的半线性椭圆边值问题的多解性[J].兰州大学学报（自然科学版）,1993,29(3):32-37.
-
9邓引斌.一类半线性椭圆边值问题k-波节解的唯一性[J].华中师范大学学报（自然科学版）,1990,24(2):131-138.
-
10柯晓峰,唐春雷.共振p-Laplacian方程解的存在性(英文)[J].西南大学学报（自然科学版）,2008,30(6):21-26. 被引量：2
