Strictly positive solutions for one-dimensional nonlinear problems involving the p-laplacian

Abstract

Let Ω be a bounded open interval, and let p>1 and q∈(0,p−1). Let m∈Lp′(Ω) and 0≤c∈L∞(Ω). We study the existence of strictly positive solutions for elliptic problems of the form −(|u′|^p − 2u′)′+c(x)u^(p−1)=m(x)u^q in Ω, u=0 on ∂Ω. We mention that our results are new even in the case c≡0.