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 estimates in the variable spaces setting.
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).