Positive and compacton-type solutions for a quasilinear two-point boundary value problem

In this paper we investigate a one-dimensional p-Laplacian problem, whose nonlinearity comprises both p-sublinear and p-superlinear terms. By studying the multiplicity of solutions to an auxiliary problem, we show how convenient choices of the parameters involved yield the existence of at least three classical positive solutions satisfying Hopf's boundary condition. In addition, we provide the existence of two distinct curves of parameters along which our problem admits at least a compacton-type solution.