- Volume 49 Issue 6
DOI QR Code
MULTIPLICITY OF NONTRIVIAL SOLUTIONS TO PERTURBED SCHRÖDINGER SYSTEM WITH MAGNETIC FIELDS
- Zhang, Huixing (Department of Mathematics China University of Mining and Technology) ;
- Liu, Wenbin (Department of Mathematics China University of Mining and Technology)
- Received : 2011.07.17
- Published : 2012.11.30
We are concerned with the multiplicity of semiclassical solutions of the following Schr
- A. Ambrosetti, M. Badiale, and S. Cingolani, Semiclassical states of nonlinear Schrodinger equations, Arch. Ration. Mech. Anal. 140 (1997), no. 3, 285-300. https://doi.org/10.1007/s002050050067
- A. Ambrosetti, A. Malchiodi, and S. Secchi, Multiplicity results for some nonlinear Schrodinger equations with potentials, Arch. Ration. Mech. Anal. 159 (2001), no. 3, 253-271. https://doi.org/10.1007/s002050100152
- G. Arioli and A. Szulkin, A semilinear Schrodinger equation in the presence of a magnetic field, Arch. Ration. Mech. Anal. 170 (2003), no. 4, 277-295. https://doi.org/10.1007/s00205-003-0274-5
- T. Bartsch, E. N. Dancer, and S. Peng, On mult-bump semi-classical bound states of nonlinear Schrodinger equations with electromagnetic fields, Adv. Differential Equations 11 (2006), no. 7, 781-812.
- V. Benci, On critical point theory for indefinite functionals in the presence of symmetries, Trans. Amer. Math. Soc. 274 (1982), no. 2 533-572.
- D. Cao and Z. Tang, Existence and uniqueness of multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields, J. Differential Equations 222 (2006), no. 2, 381-424. https://doi.org/10.1016/j.jde.2005.06.027
- S. Cingolani, Semiclassical stationary states of nonlinear Schrodinger equation with an external magnetic field, J. Differential Equations 188 (2003), no. 1, 52-79. https://doi.org/10.1016/S0022-0396(02)00058-X
- S. Cingolani and M. Lazzo, Multiple positive solutions to nonlinear Schrodinger equation with competing potential functions, J. Differential Equations 160 (2000), no. 1, 118-138. https://doi.org/10.1006/jdeq.1999.3662
- S. Cingolani and M. Nolasco, Multi-peaks periodic semiclassical states for a class of nonlinear Schrodinger equation, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 6, 1249-1260. https://doi.org/10.1017/S030821050002730X
- S. Cingolani and S. Secchi, Semiclassical states for NLS equations with magnetic potentials having polynomial growths, J. Math. Phys. 46 (2005), no. 5, 053503, 19 pp. https://doi.org/10.1063/1.1874333
- M. Clapp and Y. H. Ding, Minimal nodal solutions of a Schrodinger equation with critical nonlinearity and symmetric potential, Differential Integral Equations 16 (2003), no. 8, 981-992.
- Y. H. Ding and F. H. Lin, Solutions of perturbed Schrodinger equations with critical nonlinearity, Calc. Var. Partial Differential Equations 30 (2007), no. 2, 231-249. https://doi.org/10.1007/s00526-007-0091-z
- M. Esteban and P. L. Lions, Stationary solutions of nonlinear Schrodinger equation with an external magnetic field, in PDE and Calculus of Variations, in honor of E. De Giorgi, Brikhauser, 1990, 369-408.
- A. Floer and A. Weinstein, Nonspreading wave packets for the cubic Schrodinger equation with a bounded potential, J. Funct. Anal. 69 (1986), no. 3, 397-408. https://doi.org/10.1016/0022-1236(86)90096-0
- Y. G. Oh, On positive multi-lump bound states of nonlinear Schrodinger equations under multiple well potential, Comm. Math. Phys. 131 (1990), no. 2, 223-253. https://doi.org/10.1007/BF02161413
- M. del Pino and P. Felmer, Semi-classical states for nonlinear Schrodinger equations, J. Funct. Anal. 149 (1997), no. 1, 245-265. https://doi.org/10.1006/jfan.1996.3085
- M. del Pino and P. Felmer, Multi-peak bound states for nonlinear Schrodinger equations, Ann. Inst. H. Poincare Anal. Non Lineaire 15 (1998), no. 2, 127-149. https://doi.org/10.1016/S0294-1449(97)89296-7
- Z. Tang, On the least energy solutions of nonlinear Schrodinger equations with electromagnetic fields, Comput. Math. Appl. 54 (2007), no. 5, 627-637. https://doi.org/10.1016/j.camwa.2006.12.031
- Z. Tang, Multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields and critical frequency, J. Differential Equations 245 (2008), no. 10, 2723- 2748. https://doi.org/10.1016/j.jde.2008.07.035
- F. Wang, On an electromagnetic Schrodinger equation with critical growth, Nonlinear Anal. 69 (2008), no. 11, 4088-4098. https://doi.org/10.1016/j.na.2007.10.039
- X. Wang, On concentration of positive bound states of nonlinear Schrodinger equations, Comm. Math. Phys. 153 (1993), no. 2, 229-244. https://doi.org/10.1007/BF02096642
- M. Willem, Minimax Theorems, Birkhauser, Boston, MA, 1996.