Radial solutions with a prescribed number of zeros for a superlinear Dirichlet problem in annular domain

Abstract

In this article we study the existence of radially symmetric solutions to a superlinear Dirichlet problem in annular domain in $\mathbb{R}^N$. Using fairly straightforward tools of the theory of ordinary differential equations, we show that if k is a sufficiently large nonnegative integer, there is a solution u which has exactly (k-1) interior zeros.

Keywords

• Superlinear
• radial solution
• Bessel's equation