Geodesic
Multiple solutions for perturbed non-local fractional Laplacian equations
Electronic journal of differential equations, Tome 2013 (2013)
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},
     year = {2013},
     volume = {2013},
     zbl = {1290.35309},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a36/}
}
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AU  - Guerrini,  Luca
AU  - Zhang,  Binlin
TI  - Multiple solutions for perturbed non-local fractional Laplacian equations
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
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%A Guerrini,  Luca
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%J Electronic journal of differential equations
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%F EJDE_2013__2013__a36
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/