Positive solutions for a class of nonresonant boundary-value problems

Abstract

This paper concerns the existence and multiplicity of positive solutions to the nonresonant second-order boundary-value problem Lx = λw(t)ƒ(t, x). We are interested in the operator Lx := -x″ + ρqx when w is in Lp for 1 ≤ p ≤ +∞. Our arguments are based on fixed point theorems in a cone and Hölder's inequality. The nonexistence of positive solutions is also studied.