A bounded resonant problem for the elliptic equation involving the square root of the Laplacian

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Abstract

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.

Keywords

the square root of the Laplacian / critical groups / morse theory / resonance / local linking

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