Radial solutions for the bilaplacian equation with vanishing or singular radial potentials

Abstract

Given three measurable functions $V\left(r\right)\ge 0$, $K\left(r\right)>0$ and $Q\left(r\right)\ge 0$, $r>0$, we consider the bilaplacian equation \[ Δ^2 u+V(|x|)u=K(|x|)f(u)+Q(|x|) \quad \text{in }\,\mathbb{R}^N \] and we find radial solutions thanks to compact embeddings of radial spaces of Sobolev functions into sum of weighted Lebesgue spaces.

This document continues the project of arXiv:1403.3803, arXiv:1506.00056 and arXiv:1609.05556