On a sublinear nonlocal fractional problem - Molica Bisci, Giovanni; Servadei, Raffaella (Nonlinear Analysis: Modelling and Control, 2025)
This paper deals with existence results of nonnegative solutions for a one-parameter sublinear elliptic boundary-value problem driven by the classical fractional Laplacian operator. The existence of a weak solution for any parameter λ beyond the first resonance has been proved by using a slight variation of the classical Mountain Pass result due to Ambrosetti and Rabinowitz.
Keywords: variational methods; fractional Laplacian operator; weak solutions; deformation lemma