A CURVE OF POSITIVE SOLUTIONS FOR AN INDEFINITE SUBLINEAR DIRICHLET PROBLEM

We investigate the existence of a curve q bar right arrow u(q) , with q is an element of (0, 1), of positive solutions for the problem (P-a,P-q) {-Delta u = a(x)u(q )in Omega, u = 0 on partial derivative Omega, where Omega is a bounded and smooth domain of R-N and a : Omega -> R is a sign-changing function (in which case the strong maximum principle does not hold). In addition, we analyze the asymptotic behavior of u(q) as q -> 0(+) and q -> 1(-). We also show that in some cases u(q) is the ground state solution of (P-a,P-q). As a byproduct, we obtain existence results for a singular and indefinite Dirichlet problem. Our results are mainly based on bifurcation and sub-supersolutions methods.