Work

A global compactness result for quasilinear elliptic problems with critical Sobolev nonlinearities and Hardy potentials on R^N

Year: 2024

Type: article

Abstract: In this article, we study the elliptic equation with critical Sobolev nonlinearity and Hardy potentials $$ (-\Delta)_p u+a(x) |u|^{p-1}u-\mu\frac{|u|^{p-1}u}{|x|^p} =|u|^{p^*-2}u+f(x,u),\quad u \in W^{1,p}(\mathbb{R}^N), $$ where $0<\mu<\min\{\frac{(N-p)^p}{p^p}, \frac{N^{p-1}(N-p^2)}{p^p}\}$, $p^*=\frac{Np}{N-p}$ is the critical Sobolev exponent. Through a compactness analysis of the associated functional operator, we obtain the existence of positive solutions under certain assumptions on $a(x)$ and $f(x,u)$. For more information see https://ejde.math.txstate.edu/Volumes/2024/79/abstr.html

Source: Electronic Journal of Differential Equations

DOI: 10.58997/ejde.2024.79

Authors: Lingyu Jin, Suting Wei

Institution: South China Agricultural University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G396761040