Advances in Differential Equations
- Adv. Differential Equations
- Volume 12, Number 9 (2007), 961-993.
On the superlinear Lazer-McKenna conjecture: the non-homogeneous case
E. N. Dancer and Sanjiban Santra
Abstract
We prove the Lazer-McKenna conjecture for the superlinear elliptic problem of the Ambrosetti-Prodi type with a non-homogeneous non-linearity by constructing solutions with sharp peaks. We also compute the critical groups provided the critical points are isolated.
Article information
Source
Adv. Differential Equations Volume 12, Number 9 (2007), 961-993.
Dates
First available in Project Euclid: 18 December 2012
Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867420
Mathematical Reviews number (MathSciNet)
MR2351835
Zentralblatt MATH identifier
1162.35037
Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B25: Singular perturbations 35J35: Variational methods for higher-order elliptic equations 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory 47J10: Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 58E07: Abstract bifurcation theory
Citation
Dancer, E. N.; Santra, Sanjiban. On the superlinear Lazer-McKenna conjecture: the non-homogeneous case. Adv. Differential Equations 12 (2007), no. 9, 961--993. https://projecteuclid.org/euclid.ade/1355867420
