Multiple solutions for a class of problems involving the p(x)-Laplacian operator

ABSTRACT

In this paper we obtain an existence result for an wide class of problems involving variable exponents which are related to several applications in electrorheological fluids and image processing. Under additional conditions it is obtained the multiplicity of solutions. It is also presented examples of applicability of the results. The arguments are based on sub-supersolutions and appropriated $L^{\mathrm{\infty }}$ estimates in the variable spaces setting.

Keywords:

• $p\left(x\right)$-Laplacian
• sub-supersolutions
• variable exponents
• existence

2010 Mathematics Subject Classifications:

• 35J60
• 35J70

Acknowledgments

The authors want to thank the anonymous referee whose report has greatly helped them to improve this paper.

Disclosure statement

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

Additional information

Funding

The first author was supported by CAPES/Brazil.