The study of Nonnegative Solutions for a Class of p-Laplacian Boundary Value Problems with Dirichlet Boundary Conditions

We consider the boundary value problem where λ > 0 is a parameter and p > 1, and is the conjugate exponent of p and φ_p(x):=|x|^p−2x for all x ∈ R where (φ_p(u′))′ is the one dimensional p-Laplacian and f ∈ C²[0, ∞), and also f is monotonically increasing and concave up such that f (0) < 0. In this paper we study for the cases ρ = θ and ρ ∈ (θ, ∞) (ρ is the supremum of the nonnegative solution and, θ is such that, . We discuss existence and multiplicity results for nonnega tive solutions.