In this work, we study the existence and multiplicity of solutions to the problem $$\displaylines{ -(\Delta)_p^s u + V(x)|u|^{p-2}u = \lambda f(u),\quad x\in\Omega;\cr u=0,\quad x\in R^N\backslash\Omega, }$$ where \(\Omega\subset R^N\) is an open bounded set with Lipschitz boundary \(\partial\Omega\), \(N\geq 2\), \(V\in L^{\infty}(R^N)\), and \((-\Delta)_p^s\) denotes the fractional p-Laplacian with \(s\in(0,1)\), \(1
Submitted July 15, 2024. Published November 11, 2024.
Math Subject Classifications: 35J20.
Key Words: Mountain pass theorem; Morse theory; critical groups; comparison principle.
DOI: 10.58997/ejde.2024.72
Show me the PDF file (463 KB), TEX file for this article.
 |
Emer Lopera Universidad Nacional de Colombia Manizales, Colombia email: edloperar@unal.edu.co |
|---|---|
 |
Leandro Recôva California State Polytechnic University 3801 West Temple Avenue, Pomona, CA 91768, USA email: llrecova@cpp.edu |
 |
Adolfo Rumbos Pomona College Mathematics and Statistics Department 610 N. College Avenue, Claremont, CA 91711, USA email: arumbos@pomona.edu |
Return to the EJDE web page