We consider the following Choquard equationwhere λ is a real parameter, 2is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality. Under some suitable assumptions on λ, µ, via the constrained minimizer method and concentration compactness principle, we prove that this system has multiple of solutions, and one of which is a positive ground state solution. Moreover, by using an abstract result due to K.-C Chang, we admit infinitely many pairs of distinct solutions. In addition, we prove the nonexistence result by Pohožaev identity when λ < 0. The main results extend and complement the earlier works in the literature.
We study a nonlinear Choquard equation with weighted terms and critical Sobolev-Hardy exponent. We apply variational methods and Lusternik-Schnirelmann category to prove the multiple positive solutions for this problem.
In this paper, we consider the quasilinear elliptic equation with singularity and critical exponentsis a critical Sobolev-Hardy exponent. We deal with the existence of multiple solutions for the above problem by means of variational and perturbation methods.
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