NONNEGATIVE SOLUTIONS OF AN INDEFINITE SUBLINEAR ROBIN PROBLEM II: LOCAL AND GLOBAL EXACTNESS RESULTS

We proceed further in the investigation of the Robin problem (P-alpha) {-Delta u = a(x)uq in Omega, u >= 0 in Omega, partial derivative(v)u = alpha u on partial derivative Omega, on a smooth bounded domain Omega subset of R-N, with a sign-changing and 0< q< 1. Assuming the existence of a positive solution for alpha = 0 (which holds if q is close enough to 1), we sharpen the description of the nontrivial solution set of (P-alpha) for alpha > 0. Moreover, strengthening the assumptions on a and q we provide a global (i.e., for every alpha > 0) exactness result on the number of solutions of (P-alpha). Our approach also applies to the problem (S alpha) {-Delta u = alpha(u) + a(x)u(q) in Omega, u >= 0 in Omega, partial derivative(v)u = alpha u on partial derivative Omega,