Intertwining solutions for magnetic relativistic Hartree type equations
Intertwining solutions for magnetic relativistic Hartree type equations
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DOI：
10.1088/1361-6544/aab0be
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发表时间：
2018-04
期刊：
影响因子：
1.7
通讯作者：
S. Cingolani;S. Secchi
中科院分区：
文献类型：
--
作者：
S. Cingolani;S. Secchi
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.
