Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent

By Jean Van Schaftingen, Jiankang Xia. Journal of Mathematical Analysis and Applications, 2017

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Abstract We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation − Δ u + u = ( I α ⁎ | u | α N + 1 ) | u | α N − 1 u + f ( x , u )  in  R N where N ≥ 1 , I α is the Riesz potential of order α ∈ ( 0 , N ) , the exponent α N + 1 is critical with respect to the Hardy–Littlewood–Sobolev inequality and the nonlinear perturbation f satisfies suitable growth and structural assumptions.

Subfields: Applied Mathematics, Mathematical Physics

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