In this paper we show that a class of superlinear boundary value problems in annular domains have infinitely many radially symmetric solutions. The result is obtained without other restrictions on the growth of the nonlinearities. Our methods rely on the energy analysis and the phase plane angle analysis of the solutions for the associated ordinary differential equations.
In this paper, we establish the existence of positive radially symmetric solutions of div(|Du|p-2Du) + λf(r,u(r) ) = 0 in domain R1 < r < R0 or 0 < r < ∞ with a variety of Dirichlet boundary conditions. The function f is allowed to be singular when u = 0.
