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In this paper, using a change of variables and variational method, positive solutions of the stationary relativistic nonlinear Schrödinger equation involving critical exponent and Hardy potential are studied when the potential function has positive lower bound and radial symmetry. We extend the result of Huang, Xiang (Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Commun Pure Appl Anal. 2016;15(4):1309–1333.) to equation with Hardy potential. But, it seems difficult to get solutions for our problem inby perturbation approach as them since the existence of Hardy potential term.

Positive solutions for a relativistic nonlinear Schrödinger equation with critical exponent and Hardy potential