This article studies the existence of solutions for the fractional p-Laplacian problem $$\displaylines{ (-\Delta)_p^su=\lambda|u|^{q-2}u+ \frac{|u|^{r-2}u}{|x|^\alpha}, \quad \hbox{in } \Omega,\cr {N}_{s,p}u(x)+\beta(x)|u|^{p-2}u=0, \quad\hbox{in }\mathbb{R}^n\backslash\Omega, }$$ where \(\Omega\) is a smooth bounded domain in \({\mathbb{R}}^n\) containing \(0\) with smooth boundary, \((-\Delta)_p^s\) denotes the fractional p-Laplace operator and \(\lambda>0\), \(1
Math Subject Classifications: 35R11, 35S15, 35A15, 47G20.
Key Words: Fractional p-Laplacian; Nehari manifold; Robin boundary; Hardy-Sobolev exponent.
DOI: 10.58997/ejde.2025.13
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Junhui Xie School of Mathematics and Statistics Hubei University of Education Wuhan, 430205, Hubei, China email: smilexiejunhui@hotmail.com |
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Pengfei Li School of Mathematics and Statistics Fuzhou University Fuzhou, 350108, Fujian, China email: pfliyou@163.com |
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