Existence in the nonlinear Schr\"odinger equation with bounded magnetic field

DOI10.1007/S00030-022-00763-6zbMath1530.35244arXiv2111.05362MaRDI QIDQ6382623

Kyril Tintarev, Ian Schindler

Publication date: 9 November 2021

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence theories for optimal control problems involving partial differential equations (49J20) Compactness in Banach (or normed) spaces (46B50) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Variational methods for second-order elliptic equations (35J20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Semilinear elliptic equations (35J61) Pattern formations in context of PDEs (35B36)

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