Positive radial solutions for elliptic equations with nonlinear gradient terms in an annulus

Abstract

This paper deals with the existence of positive radial solutions of the elliptic equation with nonlinear gradient termwhere , , is continuous. Under the conditions that the nonlinearity may be of superlinear or sublinear growth in u and , existence results of positive radial solutions are obtained. For the superlinear case, the growth of f in is restricted to quadratic growth. The superlinear and the sublinear growth of the nonlinearity of f are described by inequality conditions instead of the usual upper and lower limits conditions. Our discussion is based on the fixed point index theory in cones.