On the structure of positive radial solutions for quasilinear equations in annular domains

Abstract

We study the existence, multiplicity and nonexistence of positive radial solutions to boundary value problems for the quasilinear equation $\text{ div} \left ( A(| \nabla u|)\nabla u \right ) + \lambda h(|x|)f(u) =0$ in annular domains under general assumptions on the function $A(u)$. Various possible behaviors of the quotient $\frac{f(u)}{A(u)u}$ at zero and infinity are considered. We shall use fixed point theorems for operators on a Banach space.