Entropy solutions for elliptic Schrodinger type equations under Fourier boundary conditions

This article is concerned with the study of entropy solutions to nonlinear Schrodinger-type equation of the form {div (a(x,vertical bar del u vertical bar)del u) + vertical bar u vertical bar(p(x)-2)u = f(x,u) in Omega lambda u+a(x, vertical bar del u vertical bar)del u.eta = g on partial derivative Omega, where Omega is a bounded open subset in R-N (N >= 3) with Lipschitz boundary partial derivative Omega, eta is the outer unit normal vector on partial derivative Omega, the exponent p(.) is a continuous function such that 1 < p(x) < N and lambda > 0. Under a suitable condition on f and g is an element of L-1 (partial derivative Omega), we prove the existence of entropy solutions for a Schrodinger type equation in the context of Sobolev spaces with variable exponents.