Entire solutions for a class of elliptic equations involving $p$-biharmonic operator and Rellich potentials

Abstract

We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to p-biharmonic type equations with weights. More precisely, we deal with the following family of equations $${\Delta }_p^{2}u=\lambda |x{|}^{-2p}|u{|}^{p-2}u+|x{|}^{-\beta }|u{|}^{q-2}u\text{in}{\mathbb{R}}^N,$$ where $N>2p$, $p>1$, $q>p$, $\beta =N-\frac{q}{p}(N-2p)$ and $\lambda \in \mathbb{R}$ is smaller than the Rellich constant.

12 pages

References in corpus (1)

• Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials

Cited by in corpus (1)

• Singular $p$-biharmonic problem with the Hardy potential