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Ground state solution for a class of Choquard equation with indefinite periodic potential. (English) Zbl 1491.35236

Summary: This paper is concerned with a class of nonlinear Choquard equation with potential. We assume the potential satisfies general indefinite periodic condition, so the Schrödinger operator has purely continuous spectrum and the associate energy functional is strongly indefinite. Applying the generalized Nehari manifold method developed by Szulkin and Weth, we prove the existence of ground state solution.

MSC:

35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A15 Variational methods applied to PDEs
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