Radial symmetric solution of a nonlinear fourth order elliptic equation on annular domains
This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation β³2π’=π(π’,β³π’) on an annular domain Ω in βπ with the Navier boundary conditions π’|∂Ω=0 and β³π’|∂Ω=0, where π:β+×β−→β+ is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow π(π,π) to have superlinear or sublinear growth on π,π as |(π,π)|→0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones.