Positive Solutions to Nonlinear Elliptic Equations Depending on a Parameter with Dirichlet Boundary Conditions

Abstract

The authors prove some new results on the existence of positive radial solutions to the elliptic equation $$-\Delta u= \lambda h(|x|,u)$$ in an annular domain in $${\mathbb {R}}^{N}, N\ge 2$$ . Existence of positive radial solutions are determined under the conditions that the nonlinearity h(t, u) is of either superlinear or sublinear growth in u or satisfies some upper and lower inequalities on h. Their approach is based on a revised version of a fixed point theorem of Gustafson and Schmitt.