Ground State Solutions for Schrodinger Equations in the Presence of a Magnetic Field
DOI:
https://doi.org/10.33044/revuma.3834Abstract
This paper is dedicated to studying the schrodinger equations in the presence of a magnetic field. Based on variational methods, especially Mountain Pass Theorem, we obtain ground state solutions for the system under certain assumptions.
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A. Ambrosetti, V. Felli, and A. Malchiodi, Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity, J. Eur. Math. Soc. (JEMS) 7 no. 1 (2005), 117–144. DOI MR Zbl
V. Ambrosio, Multiplicity and concentration results for fractional Schrödinger–Poisson equations with magnetic fields and critical growth, Potential Anal. 52 no. 4 (2020), 565–600. DOI MR Zbl
G. Arioli and A. Szulkin, A semilinear Schrödinger equation in the presence of a magnetic field, Arch. Ration. Mech. Anal. 170 no. 4 (2003), 277–295. DOI MR Zbl
M. Badiale and G. Tarantello, A Sobolev–Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics, Arch. Ration. Mech. Anal. 163 no. 4 (2002), 259–293. DOI MR Zbl
J. Batt, W. Faltenbacher, and E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal. 93 no. 2 (1986), 159–183. DOI MR Zbl
Z. Binlin, M. Squassina, and Z. Xia, Fractional NLS equations with magnetic field, critical frequency and critical growth, Manuscripta Math. 155 no. 1-2 (2018), 115–140. DOI MR Zbl
J. Byeon and Z.-Q. Wang, Standing wave solutions with a critical frequency for nonlinear Schrödinger equations, in Topological methods, variational methods and their applications (Taiyuan, 2002), World Scientific, River Edge, NJ, 2003, pp. 45–52. MR Zbl
P. d'Avenia and J. Mederski, Positive ground states for a system of Schrödinger equations with critically growing nonlinearities, Calc. Var. Partial Differential Equations 53 no. 3-4 (2015), 879–900. DOI MR Zbl
P. d'Avenia and M. Squassina, Ground states for fractional magnetic operators, ESAIM Control Optim. Calc. Var. 24 no. 1 (2018), 1–24. DOI MR Zbl
A. Fiscella, A. Pinamonti, and E. Vecchi, Multiplicity results for magnetic fractional problems, J. Differential Equations 263 no. 8 (2017), 4617–4633. DOI MR Zbl
Z. Guo, M. Melgaard, and W. Zou, Schrödinger equations with magnetic fields and Hardy–Sobolev critical exponents, Electron. J. Differential Equations (2017), article no. 199. MR Zbl
H. Leinfelder, Gauge invariance of Schrödinger operators and related spectral properties, J. Operator Theory 9 no. 1 (1983), 163–179. MR Zbl
X. Shang and J. Zhang, Existence and concentration of ground states of fractional nonlinear Schrödinger equations with potentials vanishing at infinity, Commun. Contemp. Math. 21 no. 6 (2019), article no. 1850048. DOI MR Zbl
J. Sun, T.-f. Wu, and Z. Feng, Multiplicity of positive solutions for a nonlinear Schrödinger–Poisson system, J. Differential Equations 260 no. 1 (2016), 586–627. DOI MR Zbl
M. Willem, Minimax theorems, Progress in Nonlinear Differential Equations and their Applications 24, Birkhäuser Boston, Boston, MA, 1996. DOI MR Zbl
X.-J. Zhong and C.-L. Tang, Ground state sign-changing solutions for a Schrödinger–Poisson system with a critical nonlinearity in $R^3$, Nonlinear Anal. Real World Appl. 39 (2018), 166–184. DOI MR Zbl
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