Multiple solutions for a system involving an anisotropic variable exponent operator

Abstract

Abstract In this paper, the existence of a solution for an anisotropic variable exponent system is obtained and proved under general hypotheses. By considering additional conditions, it is proved a multiplicity result. The proofs are based on an application of appropriated L ∞ $L^{\infty }$ estimates, a sub-supersolution argument, and the Mountain Pass Theorem.

Keywords

• Anisotropic problem
• Electrorheological fluids
• Maximum principle
• Variable exponents
• Weak solution
• Sub-supersolutions