Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian

ABSTRACT

The paper focuses on a Dirichlet problem driven by the $\left(p\right(x),q(x\left)\right)$-Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.

Keywords:

• $\left(p\left(x\right),q\left(x\right)\right)$-Laplacian
• critical points
• multiple solutions
• Dirichlet problem

2010 Mathematics Subject Classifications:

• 35J40
• 35J60
• 35J65

Acknowledgments

The authors have been partially supported by the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The paper is partially supported by PRIN 2017- Progetti di Ricerca di rilevante Interesse Nazionale, ‘Nonlinear Differential Problems via Variational, Topological and Set-valued Methods’ (2017AYM8XW).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors have been partially supported by the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The paper is partially supported by PRIN 2017- Progetti di Ricerca di rilevante Interesse Nazionale, ‘Nonlinear Differential Problems via Variational, Topological and Set-valued Methods’ (2017AYM8XW).