含非线性凸函数的椭圆方程的多解存在性(英文)

Multiplicity of positive solutions for elliptic equations with convex nonlinearity

下载PDF

导出

摘要研究含非线性凸函数的椭圆方程的狄利克雷边值问题.应用直接和Nehari-type的变分方法,得到多解存在性结果. This work is concerned with semilinear elliptic equation subject to homogeneous Dirichlet boundary conditions. By using Direct and Nehari - type variational method, we get some multiplicity results of positive solutions.

作者戴清平徐本龙

机构地区上海师范大学数理学院

出处《上海师范大学学报（自然科学版）》 2010年第1期24-29,共6页 Journal of Shanghai Normal University(Natural Sciences)

基金 Supported by the Science Foundation of Shanghai Municipal Education Commission(No 06DZ004) Innovational Program of Shanghai Normal University.

关键词半线性椭圆方程多解 Nehari变分方法 semilinear elliptic equations multiplicity of solutions Nehari variational method

分类号 O175.25 [理学—基础数学]

引文网络
相关文献

参考文献1

1Benlong XU Zhongliang WANG.On S-Shaped Bifurcation Curves for a Class of Perturbed Semilinear Equations[J].Chinese Annals of Mathematics,Series B,2008,29(6):641-662. 被引量：2

二级参考文献25

1Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach space, SIAM Rev., 18, 1976, 620-709.
2Bebernes, J. and Eberly, D., Mathematical Problems from Combustion Theory, Springer-Verlag, Berlin/New York, 1989.
3Brown, K. J., Ibrahim, M. M. and Shivaji, R., S-Shaped bifurcation curves, Nonlinear Anal., 5, 1981, 475-486.
4Castro, A., Gadam, S. and Shivaji, R., Branches of radial solutions for semipositone problems, J. Diff. Eqs., 120, 1995, 30-45.
5Crandall, M. G. and Rabinowitz, P. H. Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal., 52, 1973, 161-180.
6Dancer, E. N., On the structure of solutions of an equation in catalysis theory when a parameter is large, J. Diff. Eqs., 37, 1980, 404-437.
7Deimling, K., Nonlinear Functional Analysis, Springer-Verlag, Berlin/New York, 1985.
8Du, Y. Exact multiplicity and S-shaped bifurcation curve for some semilinear elliptic problems from combustion theory, SIAM J. Math. Anal., 32, 2000, 707-733.
9Du, Y. and Lou, Y., Proof of a conjecture for the perturbed Gelfand equation from combustion theory, J. Diff. Eqs. 173, 2001, 213--230.
10Gidas, B., Ni, W.-M. and Nirenberg, L., Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68, 1979, 209-243.

共引文献1

1徐本龙,王中亮.一类半线性椭圆方程及其摄动方程解的确切个数和分歧结构[J].应用数学学报,2009,32(3):431-444.

1Shou Feng WANG.Quasi-Type δ Semigroups with an Adequate Transversal[J].Journal of Mathematical Research and Exposition,2011,31(6):1129-1135.
2赵守江,刘巧静.同分布PA序列的强大数定律[J].河北工业大学学报,2011,40(1):76-78.
3Yu WU.Nonlinear Discrete Inequalities of Bihari-type and Applications[J].Acta Mathematicae Applicatae Sinica,2013,29(3):603-614.
4Stojan RADENOVIC,Peyman SALIMI,Calogero VETRO,Tatjana DOSENOVIC.EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS[J].Acta Mathematica Scientia,2016,36(1):94-110. 被引量：1
5Fridoun MORADLOU,Peyman SALIMI,Pasquale VETRO.SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES[J].Acta Mathematica Scientia,2013,33(4):1049-1058. 被引量：3
6宋传静,张毅.Perturbation to Mei Symmetry and Adiabatic Invariants for Disturbed El-Nabulsi's Fractional Birkhoff System[J].Communications in Theoretical Physics,2015(8):171-176. 被引量：4
7曹飞龙,林绍波.MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS[J].Acta Mathematica Scientia,2012,32(2):471-482.
8Jincun LIU,Hong LI,Yang LIU,Zhichao FANG.Reduced-order finite element method based on POD for fractional Tricomi-type equation[J].Applied Mathematics and Mechanics(English Edition),2016,37(5):647-658. 被引量：1
9杨云青,王云虎,李昕,程雪苹.Riccati-type Backlund transformations of nonisospectral and generalized variable-coefficient KdV equations[J].Chinese Physics B,2014,23(3):186-192.
10WANG XUE-JUN SHEN YAN HU SHU-HE YANG WEN-ZHI.Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications[J].Communications in Mathematical Research,2011,27(1):6-16.

上海师范大学学报（自然科学版）

2010年第1期

浏览历史

内容加载中请稍等...

含非线性凸函数的椭圆方程的多解存在性(英文)

参考文献1

二级参考文献25

共引文献1

相关作者

相关机构

相关主题

浏览历史