POSITIVE SOLUTIONS FOR CHOQUARD EQUATION IN EXTERIOR DOMAINS

This work concerns with the following Choquard equation { -Delta u + u = (integral(Omega) u(2) (y)/vertical bar x -y vertical bar(N) (-2) dy)u in Omega, u is an element of H-0(1) ( Omega), where Omega subset of R-N is an exterior domain with smooth boundary. We prove that the equation has at least one positive solution by variational and toplogical methods. Moreover, we establish a nonlocal version of global compactness result in unbounded domain.

Automated summary

This work proves the existence of at least one positive solution to the Choquard equation using variational and topological methods, as well as establishes a nonlocal version of global compactness result in an unbounded domain.