Multiplicity results for a class of singular elliptic equation involving sublinear Neumann boundary condition in

Let be a bounded domain with boundary of class . The purpose of this paper is to study the existence of positive solution for the following inhomogeneous singular Neumann problem: (P-mu,lambda) {-Delta u + u = mu u(-delta) + h(x, u)e(ua), u > 0 in Omega, partial derivative u/partial derivative nu = lambda psi u(q) on partial derivative Omega. where mu, lambda > 0, 0 < delta < 3, 1 <= alpha <= 2, 0 <= q < 1, and psi is a non-negative Holder continuous function on Here, h(x, u) is a C-1 (<(Omega)over bar> x R)having superlinear growth at infinity. Using variational methods, we show that there exists a region R subset of {(mu, lambda) : mu, lambda > 0} bounded by the graph of a map., such that (P-mu, lambda) admits at least two solutions for all (mu, lambda) is an element of R, at least one solution for (mu, lambda) is an element of partial derivative R and no solution for all (mu, lambda) outside (R) over bar.