Existence Of Radial Solutions For Elliptic Equations With Gradient Terms In Annular Domains

In this paper,we deal with the existence of radial solutions for the elliptic equation with gradient (?), in annular domain {x?RN|r1<|x|<r2},where N ? 3 and f:[r1,r2]×R ×R+?R are continuous.The main results of this paper are as follows1.Under the condition that the nonlinear term satisfies linear growth,using Leray-Schauder fixed point theorem of full continuous operator,we obtain the exis-tence of radial solutions2.For the case of superlinear growth on one side of the nonlinear term f(r,u,?),under the condition that f(r,u,?)satisfies Nagumo-type growth conditions on ?,using Leray-Schauder fixed point theorem,the existence of its radial solutions is given;3.Through using the method of upper and lower solutions and a truncating functional technique,we obtain the existence of radial solutions4.When f satisfies the appropriate inequality conditions,applying the general-ization theorem of the fixed point theorem,see[53].We get the existence of positive radial solutions for the elliptic equation with gradient in annular domainsIn each part,we give a corresponding example to illustrate the application of our conclusions.