Asymptotic expansion of solutions to nonlinear elliptic eigenvalue problems

We consider the nonlinear eigenvalue problem -Delta(u) + g(u) = lambda sinu in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N (N >= 2) is an appropriately smooth bounded domain and lambda > 0 is a parameter. It is known that if lambda >> 1, then the corresponding solution u. is almost. at and almost equal to p inside.. We establish an asymptotic expansion of u(lambda)(x) (x is an element of Omega) when lambda >> 1, which is explicitly represented by g.