Geodesic
Perturbed Problems Involving the Square Root of the Laplacian
Minimax theory and its applications, Tome 4 (2019) no. 1
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We prove multiplicity of solutions for perturbed problems involving the square root of the Laplacian ∆1/2. More precisely, we consider the problem { u λu fx,u εgx,u inΩ uon ∂Ω, where Ω RN is a bounded domain, ε R, N > , f is a subcritical function with asymptotic linear behavior at infinity, and g is a continuous function. We also show the invariance under small perturbations of the number of distinct critical levels of the associated energy functional to the unperturbed problem, in both resonant and non-resonant case.
Mots-clés : Fractional Laplacian, variational methods, multiplicity of solutions 
@article{MTA_2019_4_1_a2,
     author = {Rossella Bartolo and Eduardo Colorado,Giovanni Molica Bisci},
     title = {Perturbed {Problems} {Involving} the {Square} {Root} of the {Laplacian}},
     journal = {Minimax theory and its applications},
     year = {2019},
     volume = {4},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/MTA_2019_4_1_a2/}
}
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Rossella Bartolo; Eduardo Colorado,Giovanni Molica Bisci. Perturbed Problems Involving the Square Root of the Laplacian. Minimax theory and its applications, Tome 4 (2019) no. 1. http://geodesic.mathdoc.fr/item/MTA_2019_4_1_a2/