학술논문
Existence, nonexistence, and multiplicity of solutions for the fractional $p&q$-Laplacian equation in $\Bbb R^N$.
Document Type
Journal
Author
Chen, Caisheng (PRC-HOH-SC) AMS Author Profile; Bao, Jinfeng (PRC-HOH-SC) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35A General topics
35A15Variational methods
35Partial differential equations -- 35J Elliptic equations and systems
35J60Nonlinear elliptic equations
35J92Quasilinear elliptic equations with $p$-Laplacian
35A15
35
35J60
35J92
Language
English
Abstract
Summary: ``In this paper, we study the existence, nonexistence, and multiplicity of solutions to the following fractional $p\&q$-Laplacian equation: $$\aligned &(-\Delta)^s_pu+a(x)|u|^{p-2}u+(-\Delta)^s_qu+b(x)|u|^{q-2}u + \mu (x)|u|^{r-2}u\\&\quad\ =\lambda h(x)|u|^{m-2}u,\quad x\in\Bbb R^N,\endaligned\tag{0.1}, $$ where $\lambda$ is a real parameter, $(-\Delta)^s_p$ and $(-\Delta)^s_q$ are the fractional $p\&q$-Laplacian operators with $01$ and $spMR3462564] and Chaves et al. (Nonlinear Anal. 114:133--141, 2015) [MR3300789] to the fractional $p\&q$-Laplacian equation (0.1).''