Geodesic
Multiple solutions for perturbed non-local fractional Laplacian equations
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In article we consider problems modeled by the non-local fractional Laplacian equation $$\displaylines{ (-\Delta)^s u=\lambda f(x,u)+\mu g(x,u) \quad{in } \Omega\cr u=0 \quad{in } \mathbb{R}^n\setminus \Omega, }$$ where $s\in (0,1)$ is fixed, $(-\Delta )^s$ is the fractional Laplace operator, $\lambda,\mu$ are real parameters, $\Omega$ is an open bounded subset of $\mathbb{R}^n (n>2s)$ with Lipschitz boundary $\partial \Omega$ and $f,g:\Omega\times\mathbb{R}\to\mathbb{R}$ are two suitable Caratheodory functions. By using variational methods in an appropriate abstract framework developed by Servadei and Valdinoci [17] we prove the existence of at least three weak solutions for certain values of the parameters.
Classification : 49J35, 35A15, 35S15, 47G20, 45G05
Keywords: variational methods, integrodifferential operators, fractional Laplacian 
@article{EJDE_2013__2013__a36,
     author = {Ferrara, Massimiliano and Guerrini, Luca and Zhang, Binlin},
     title = {Multiple solutions for perturbed non-local fractional {Laplacian} equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a36/}
}
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Ferrara, Massimiliano; Guerrini, Luca; Zhang, Binlin. Multiple solutions for perturbed non-local fractional Laplacian equations. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a36/