In this paper, we obtained the existence of nontrivial solutions of the nonlocal elliptic equation involving the square root of the Laplacian with asymptotic linear resonance at infinity perturbed by a bounded nonlinearity. We made use of a penalized method, local linking and Morse theory.

In this paper we study the existence of nontrivial solutions of a class of asymptotically resonant problems driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions by applying Morse theory and critical groups for a $C^2$ functional at both isolated critical points and infinity.