Advances in Differential Equations

On the superlinear Lazer-McKenna conjecture: the non-homogeneous case

E. N. Dancer and Sanjiban Santra

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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

Adv. Differential Equations, Volume 12, Number 9 (2007), 961-993.

First available in Project Euclid: 18 December 2012

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Zentralblatt MATH identifier

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


Dancer, E. N.; Santra, Sanjiban. On the superlinear Lazer-McKenna conjecture: the non-homogeneous case. Adv. Differential Equations 12 (2007), no. 9, 961--993.

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