Solvability of Parametric Elliptic Systems with Variable Exponents

Abstract

In this paper, we study the solvability to the left of the positive infimum of all eigenvalues for some non-resonant quasilinear elliptic problems involving variable exponents. We first prove the existence of at least a weak solution for some non-variational systems by using a surjectivity result for pseudomonotone operators. Furthermore, under additional conditions, we show that the solution is unique and provide examples. Second, we deal with non-resonant gradient-type systems and obtain existence by using a variational approach.

Keywords

• p(x)-laplacian
• positive infimum
• weak solution
• existence and uniqueness
• 35a15
• 35b38
• 35j62