Alessio Fiscella, Raffaella Servadei, Enrico Valdinoci
Asymptotically linear problems driven by fractional Laplacian operators
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ABSTRACT.  In this paper we study a non-local fractional Laplace equation, depending on a parameter $\lambda$\,, with asympotically linear right-hand side. Our main result concerns the existence of weak solutions for this equation and it is obtained using variational and topological methods. 
Namely, our existence theorem follows as an application of the Saddle Point Theorem. It extends some results, well known for the Laplace operator, to the non-local fractional setting.