Existence of solutions for (p, q)-Laplacian equations with an indefinite potential

ABSTRACT

By using variational methods we study the existence and multiplicity of solutions for a class of quasilinear problems driven by the $(p,q)$-Laplacian operator with Dirichlet boundary conditions and an indefinite potential.

COMMUNICATED BY:

• V. Rădulescu

KEYWORDS:

• Quasilinear elliptic problems
• $(p,q)$-Laplacian
• Dirichlet boundary condition
• subcritical nonlinearities
• fibering method
• indefinite potential

AMS SUBJECT CLASSIFICATIONS:

• 35J62
• 35J20
• 35JP30

Acknowledgements

The authors thank the referees for their very helpful suggestions.