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arXiv · 1806.01311

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

Marino Badiale·Stefano Greco·Sergio Rolando
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Abstract

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

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Marino Badiale, Stefano Greco, Sergio Rolando. 2018-06-04. Radial solutions for the bilaplacian equation with vanishing or singular radial potentials. https://arxiv.org/abs/1806.01311

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