Nodal solutions to a class of nonstandard superlinear equations on $\Bbb R^N$

Abstract

We investigate the existence of sign-changing radial solutions for a class of singular equations: $$ -\Delta u(x)+ b(|x|)u(x) = |u(x)|^{\theta-1}u(x)+h(|x|)\hspace{1cm}x\in\mathbb R^N $$ where $b(|x|)$ may change sign and behaves like $|x|^{-\alpha}$ at infinity for some $\alpha\in(0,2)$, and $\theta>1$.