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In this paper, we consider the nonlinear fractional critical equation with zero Dirichlet boundary condition , in and on , where is a positive function, is a regular bounded domain of , and , represents the spectral fractional Laplacian operator in with zero Dirichlet boundary condition. We prove a version of Morse lemmas at infinity for this problem. We also exhibit a relevant application of our novel result. More precisely, we characterize the critical points at infinity of the associated variational problem and we prove an existence result for and .
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Wael Abdelhedi, Hichem Hajaiej, Zeinab Mhamdi, A Morse lemma at infinity for nonlinear elliptic fractional equations. Rend. Sem. Mat. Univ. Padova 146 (2021), pp. 1–42DOI 10.4171/RSMUP/82