We prove the existence of a solution to the semirelativistic Hartree equation-Δ + m2u + V(x)u = A(x)(W ∗ |u|p)|u|p-2u under suitable growth assumption on the potential functions V and A. In particular, both can be unbounded from above.
Secchi, S. (2018). Existence of solutions for a semirelativistic Hartree equation with unbounded potentials. FORUM MATHEMATICUM, 30(1), 129-140 [10.1515/forum-2017-0006].
Existence of solutions for a semirelativistic Hartree equation with unbounded potentials
Secchi, S
2018
Abstract
We prove the existence of a solution to the semirelativistic Hartree equation-Δ + m2u + V(x)u = A(x)(W ∗ |u|p)|u|p-2u under suitable growth assumption on the potential functions V and A. In particular, both can be unbounded from above.
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