The existence of solutions to the nonhomogeneous \(A\)-harmonic equations with variable exponent (Q1723748)

Summary: 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 \(d^\star A(x, d \omega) = B(x, d \omega)\) in the weighted variable exponent Sobolev space \(W_d^{p(x)}(\Omega, \Lambda^l, \mu) \).