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| Existence of Nonnegative Solutions for a Class of Systems Involving Fractional (p,q)-Laplacian Operators |
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Citation： |
Yongqiang FU,Houwang LI,Patrizia PUCCI.Existence of Nonnegative Solutions for a Class of Systems Involving Fractional (p,q)-Laplacian Operators[J].Chinese Annals of Mathematics B,2018,39(2):357~372 |
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Net amount： 694 |
Authors： |
Yongqiang FU; Houwang LI;Patrizia PUCCI |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11771107), the Italian MIUR Project
Variational Methods, with Applications to Problems in Mathematical
Physics and Geometry (No.2015KB9WPT_009), the Gruppo Nazionale
per l'Analisi Matematica, la Probabilit`a e le loro Applicazioni
(GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and
the INdAM-GNAMPA Project 2017 titled Equazioni Differenziali non
lineari (No.Prot_2017_0000265). |
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| Abstract： |
The authors study the following Dirichlet problem of a system
involving fractional $(p,q)$-Laplacian operators:
$$\left\{\!\!\!\begin{array}{ll}
\ds (-\Delta)_p^s u = \lambda a(x)|u|^{p-2}u +\lambda
b(x)|u|^{\alpha-2}|v|^{\beta}u
+\frac{\mu(x)}{\alpha \delta}|u|^{\gamma-2}|v|^{\delta}u & \mbox{in
}\Omega,\\[3mm]
\ds (-\Delta)_q^s v = \lambda c(x)|v|^{q-2}v +\lambda
b(x)|u|^{\alpha}|v|^{\beta-2}v
+ \frac{\mu(x)}{\beta\gamma}|u|^{\gamma}|v|^{\delta-2}v & \mbox{in }\Omega,\u=v=0 & \mbox{on }\mathbb{R}^N\backslash\Omega,
\end{array}\right.$$
where $\lambda>0$ is a real parameter, $\Omega$ is a bounded domain
in $\mathbb{R}^N$, with boundary $\partial\Omega$ Lipschitz
continuous, $s\in(0,1)$, $1 |
Keywords： |
The Nehari manifold, Fractional $p$-Laplacian, Variational methods |
Classification： |
35R11, 35A15, 35J60, 47G20 |
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