|
|
Abstract
|
|
We consider nonlinear
Dirichlet problems driven by the p-Laplacian, which are resonant at +∞ with respect
to the principal eigenvalue. Using a variational approach based on the critical point
theory, we show that the problem has three nontrivial smooth solutions, two of which
have constant sign (one positive, the other negative). In the semilinear case, assuming
stronger regularity on the nonlinear perturbation f(z,•) and using Morse theory, we
show that the problem has at least four nontrivial smooth solutions, two of constant
sign.
|
Keywords
p-Laplacian, resonant problem, mountain
pass theorem, second deformation theorem, Morse theory
|
Mathematical Subject Classification
Primary: 35J65, 58E05
|
Milestones
Received: 5 October 2008
Revised: 27 November 2008
Accepted: 11 December 2008
|
|
|
|
|
