Positive Solutions for Nonlinear Elliptic Equations Depending on a Parameter with Dirichlet Boundary Conditions
We prove new results on the existence of positive radial solutions of the elliptic equation $-Δu= λh(|x|,u)$ in an annular domain in $\mathbb{R}^{N}, N\geq 2$. Existence of positive radial solutions are determined under the conditions that the nonlinearity function $h(t,u)$ is either superlinear or sublinear growth in $u$ or satisfies some upper and lower inequalities on $h$. Our discussion is based on a fixed point theorem due to a revised version of a fixed point theorem of Gustafson and Schmitt.
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