Positive solutions to classes of infinite semipositone (p, q)-Laplace problems with nonlinear boundary conditions

Abstract

We consider one-dimensional (p, q)-Laplace problems: ?(?(u'))' = λh(t)f(u), t∈ (0, 1), u(0) =0= au'(1) + g(λ, u(1))u(1), where λ >0, a ≥0, ?(s) :=|s|^{p?2}s +|s|^{q?2}s, 1 near infinity, we establish the existence, multiplicity and nonexistence of positive solutions. In particular, we provide a sufficient condition on f to obtain a multiplicity result for the case when lims→∞f(s)/s^{r?1}∈(0, ∞), 1 problems (p =q=2). The proofs are based on a Krasnoselskii type fixed point theorem which is fit to overcome a lack of homogeneity.