Department of Mathematics
South China Agricultural University
Guangzhou 510642, China
email: jinlingyu300@126.com
Department of Mathematics
South China Agricultural University
Guangzhou 510642, China
email: stwei@scau.edu.cn
Lingyu Jin, Suting Wei
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 \(f(x,u)\).
Submitted April 5, 2024. Published December 3, 2024.
Math Subject Classifications: 35J10, 35J20, 35J60.
Key Words: p-Laplacian; compactness; positive solution; unbounded domain; Sobolev nonlinearity.
DOI: 10.58997/ejde.2024.79
Show me the PDF file (479 KB), TEX file for this article.
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Lingyu Jin Department of Mathematics South China Agricultural University Guangzhou 510642, China email: jinlingyu300@126.com |
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Suting Wei Department of Mathematics South China Agricultural University Guangzhou 510642, China email: stwei@scau.edu.cn |
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