Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities

Abstract

We study the existence and multiplicity of positive solutions for the Dirichlet problemwhere λ > 0, 1 < q < 2, p = 2* = 2N/(N − 2), 0 ε Ω ⊂ ℝN, N ≥ 3, is a bounded domain with smooth boundary ∂Ω and f is a non-negative continuous function on $\bar{\varOmega}$. Assuming that f satisfies some hypothesis, we prove that the equation admits at least three positive solutions for sufficiently small λ.