含变号权的p-Laplcean算子的特征值问题
On the Eigenvalue Problem for p-Laplcean Operator with Indefinite Weights
DOI: 10.12677/pm.2011.12012, PDF, HTML, 下载: 3,363  浏览: 8,580 
作者: 熊辉：东莞理工学院数学教研室，东莞
关键词: p-Laplace；特征值问题；Fu ik谱；变号权
p-Laplcean; Eigenvalue Problem; Fu Ik Spectrum; Indefinite Weight
摘要: 本文研究含不定权的Hardy-Sobolev算子的特征值问题(不定权表示权函数 可以变号，并具有非平凡的正部)，讨论了第一特征值的单一性、非第一特征值的特征函数的变号性和特征值序列的无穷性。并证明了Fu ik谱中非平凡曲线的存在性。
Abstract: In this paper we study the eigenvalue problem for the -Laplcean operator with indefinite weights. The simplicity, isolation of the first eigenvalue is studied here. Furthermore, the existence of a nontrivial curve is shown in the Fu ik spectrum.
文章引用：熊辉. 含变号权的p-Laplcean算子的特征值问题[J]. 理论数学, 2011, 1(2): 54-59. http://dx.doi.org/10.12677/pm.2011.12012

参考文献

[1] A. Anane. Etude des valeurs propres et de la resonnance pour l’operateur p-laplacian. Comptes Rendus de l’Académie des Sciences, 1987, 305(6): 725-728.
[2] W. Allegretto, Y. X. Hang. A picone identity for the p-Laplacian and applications. Nonlinear Analysis TMA, 1998, 32(7): 819-830.
[3] A. Szulkin, M. Wilem. Eigenvalue problems with indefinite weights. Studia Mathematica, 1999, 135(2): 199-201.
[4] M. Cuesta. Eigenvalue problems for the p-Laplacian with indefinite weights. Electronic Journal of Differential Equations, 2001, 2001(33): 1-9.
[5] K. Sandeep. On the first Eigenfunction of a perturbed Hardy- Sobolev Operator. Nonlinear Differential Equations and Applications, 2003, 10(2): 223-253.
[6] K. Sreenadh. On the Fučik spectrum of Hardy-Sobolev Operator. Nonlinear Analysis TMA, 2002, 51(7): 1167-1185.
[7] L. Boccardo, F. Murat. Almost convergence of gradients of solutions to elliptic and parabolic equations. Nonlinear Analysis TMA, 1992, 19(6): 581-597.
[8] H. Brezis, E. Lieb. A relation between point convergence of functions and convergence of functionals. Proc. AMS, 1983, 88(3): 486-490.
[9] N. C. Adimurthi, M. Ramaswamy. An improved Hardy-Sobolev inequality and its applications. Proc. AMS, 2001, 130(2): 489- 505.
[10] D. DeFigueredo. Lectures on the Ekeland variational principle with applications and Detours. TATA Institute, New York: Springer-Verlog, 1989.
[11] A. Szulkin. Ljusternik-Schnirelmann theory on C1-manifolds. Ann. Inst. H. Poincaré, Anal. Non Linéaire, 1988, 5(2): 119-139.
[12] M. Cuesta, D. Defigueredo, and J. P. Gossez. The beginning of Fučik spectrum for p-Laplacean. Journal of Differential Equations, 2001, 2001(33): 1-9.

为你推荐