Existence of solutions for a semirelativistic Hartree equation with unbounded potentials

Simone Secchi

Existence of solutions for a semirelativistic Hartree equation with unbounded potentials

Analysis of PDEs 2017-01-12 v1

Authors: Simone Secchi

Abstract

We prove the existence of a solution to the semirelativistic Hartree equation $\sqrt{-\Delta+m^2}u+ V(x) u = A(x)\left( W * |u|^p \right) |u|^{p-2}u$ under suitable growth assumption on the potential functions $V$ and $A$ . In particular, both can be unbounded from above.

Keywords

semirelativistic Hartree equation unbounded potentials existence of solutions fractional operator nonlinear elliptic problem growth assumption

Cite

@article{arxiv.1701.02885,
  title  = {Existence of solutions for a semirelativistic Hartree equation with unbounded potentials},
  author = {Simone Secchi},
  journal= {arXiv preprint arXiv:1701.02885},
  year   = {2017}
}

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