Continuous dependence of solutions for indefinite semilinear elliptic problems

Abstract

We consider the superlinear elliptic problem −∆u + m(x)u = a(x)u p in a bounded smooth domain under Neumann boundary conditions, where m ∈ L σ (Ω), σ ≥ N/2 and a ∈ C(Ω) is a sign changing function. Assuming that the associated first eigenvalue of the operator −∆ + m is zero, we use constrained minimization methods to study the existence of a positive solution when m b is a suitable perturbation of m.