Geodesic
Bounded Solutions to Nonlinear Problems in R Involving the Fractional Laplacian Depending on Parameters
Minimax theory and its applications, Tome 2 (2017) no. 2

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The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue problems involving the fractional Laplace operator ∆s and nonlinearities that have subcritical growth. In the second part, based on a variational principle of Ricceri [17], we study a fractional nonlinear problem with two parameters and prove the existence of multiple solutions.
Mots-clés : Fractional Laplacian, nonlocal eigenvalue problems, unbounded domains, existence and regularity, multiplicity results, Ricceri’s principle 
Said El Manouni,Hichem Hajaiej,Patrick Winkert. Bounded Solutions to Nonlinear Problems in R Involving the Fractional Laplacian Depending on Parameters. Minimax theory and its applications, Tome 2 (2017) no. 2. http://geodesic.mathdoc.fr/item/MTA_2017_2_2_a3/
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     author = {Said El Manouni,Hichem Hajaiej,Patrick Winkert},
     title = {Bounded {Solutions} to {Nonlinear} {Problems} in {R} {Involving} the {Fractional} {Laplacian} {Depending} on {Parameters}},
     journal = {Minimax theory and its applications},
     year = {2017},
     volume = {2},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2017_2_2_a3/}
}
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