Twin positive solutions for fourth-order two-point boundary-value problems with sign changing nonlinearities

Abstract

A new fixed point theorem on double cones is applied to obtain the existence of at least two positive solutions to (Φp(y''(t))'' - ɑ(t)ƒ (t, y(t), y''(t)) = 0, 0 < t < 1, y(0) = y(1) = 0 = y''(0) = y''(1), where ƒ : [0, 1] x [0, ∞) x (-∞, 0] → R, ɑ ∈ L¹ ([0, 1], (0, ∞)). We also give some examples to illustrate our results.