Existence and multiplicity of positive radial solutions to the Dirichlet problem for nonlinear elliptic equations on annular domains

In this paper, we study the existence and nonexistence of monotone positive radial solutions of elliptic boundary value problems on bounded annular domains subject to local boundary condition. By using Krasnoselskii's fixed point theorem of cone expansion-compression type we show that there exists lambda* >= lambda(*) > 0 such that the elliptic equation has at least two, one and no radial positive solutions for 0 < lambda <= lambda(*), lambda(*) < lambda <= lambda and lambda > lambda* respectively. We include an example to illustrate our results.