(p,2)-equations resonant at any variational eigenvalue

ABSTRACT

We consider nonlinear elliptic Dirichlet problems driven by the sum of a p-Laplacian and a Laplacian (a $(p,2)$-equation). The reaction term at $\pm \mathrm{\infty }$ is resonant with respect to any variational eigenvalue of the p-Laplacian. We prove two multiplicity theorems for such equations.

COMMUNICATED BY:

• V. Rădulescu

KEYWORDS:

• p-Laplacian
• Laplacian
• variational eigenvalues
• resonance
• multiple solutions
• critical groups
• nonlinear regularity theory

AMS SUBJECT CLASSIFICATIONS:

• 35J20
• 35J60
• 58E05

Disclosure statement

No potential conflict of interest was reported by the authors.