Uniqueness of positive and compacton-type solutions for a resonant quasilinear problem

We study a one-dimensional p-Laplacian resonant problem with p-sublinear terms and depending on a positive parameter. By using quadrature methods we provide the exact number of positive solutions with respect to mu is an element of ]0,+infinity[. Specifically, we prove the existence of a critical value mu(1) > 0 such that the problem under examination admits: no positive solutions and a continuum of nonnegative solutions compactly supported in [0, 1] for mu is an element of ]0,mu(1)[; a unique positive solution of compacton-type for mu = mu(1) a unique positive solution satisfying Hopf's boundary condition for mu is an element of]mu(1),+infinity[.