We propose an existence result for the semirelativistic Choquard equation with a local nonlinearity in R N (formula pergented) where m > 0 and the potential V is decomposed as the sum of a Z N -periodic term and of a bounded term that decays at infinity. The result is proved by variational methods applied to an auxiliary problem in the half-space R N++1
Bieganowski, B., Secchi, S. (2019). The semirelativistic Choquard equation with a local nonlinear term. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 39(7), 4279-4302 [10.3934/dcds.2019173].
The semirelativistic Choquard equation with a local nonlinear term
Secchi S.
2019
Abstract
We propose an existence result for the semirelativistic Choquard equation with a local nonlinearity in R N (formula pergented) where m > 0 and the potential V is decomposed as the sum of a Z N -periodic term and of a bounded term that decays at infinity. The result is proved by variational methods applied to an auxiliary problem in the half-space R N++1
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