Intertwining solutions for magnetic relativistic Hartree type equations. (16th April 2018)

• Record Type: Journal Article
• Authors: Cingolani, Silvia; Secchi, Simone
• Is Part Of: Nonlinearity. Volume 31:Number 5(2018:May)
• Page Start: 2294
• Page End: 2318
• Publication Date: 2018-04-16
• Subjects: magnetic relativistic Schrödinger operator -- Hartree equation -- group action -- intertwining solutions; 35J10 -- 35Q40 -- 35Q75 -- 35S05 -- 47G30; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aab0be
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the magnetic pseudo-relativistic Schrödinger equation where, m > 0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any, the cardinality of the G -orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.