The Existence of Solutions to the Nonhomogeneous A -Harmonic Equations with Variable Exponent

Abstract EN

We first discuss the existence and uniqueness of weak solution for the obstacle problem of the nonhomogeneous A -harmonic equation with variable exponent, and then we obtain the existence of the solutions of the equation d ⋆ A ( x , d ω ) = B ( x , d ω ) in the weighted variable exponent Sobolev space W d p ( x ) ( Ω , Λ l , μ ) .