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References (11)
-
(1971)
A sharp form of an inequality by N. Trudinger -
C. Alves, Ó. JoãoMarcosdo, O. Miyagaki (2003)
On a class of singular biharmonic problems involving critical exponentsJournal of Mathematical Analysis and Applications, 277
-
H. Brezis, E. Lieb (1983)
A Relation Between Pointwise Convergence of Functions and Convergence of Functionals, 88
-
N. Ghoussoub, C. Yuan (2000)
Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponentsTransactions of the American Mathematical Society, 352
-
(2003)
Sobolev-Hardy inequality and quasilinear elliptic equations (memoir) -
(2008)
On a class of elliptic equation with critical potential and indefinite weights in R2 -
J. Azorero, I. Alonso (1998)
Hardy Inequalities and Some Critical Elliptic and Parabolic ProblemsJournal of Differential Equations, 144
-
Y.T. Shen, Y.X. Yao, Z.H. Chen (2004)
Nonlinear elliptic problems with critical potential in R 2Science in China Series A: Mathematics, 34
-
A. Szulkin, M. Willem (1991)
Eigenvalue problems with indefinite weightsStud. Math., 135
-
M. Cuesta (2001)
Eigenvalue Problems for the p-Laplacian with Indefinite Weights, 2001
-
(1996)
Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamilonian Systens, Second Edition
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-012-0131-0
- Publisher site
- See Article on Publisher Site
Abstract
The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in R N , is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone’s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Dec 13, 2011