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Multibump solutions of nonlinear Schrödinger equations with steep potential well and indefinite potential
1. | Mathematisches Institut, University of Giessen, Arndtstr. 2 35392 Giessen, Germany |
2. | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
References:
[1] |
T. Bartsch and M. Parnet, Nonlinear Schrödinger equations near an infinite potential well, arXiv:1205.1345. |
[2] |
T. Bartsch and Z. Q. Wang, Existence and multiplicity results for some superlinear ellipticequation $\mathbb{R}^N2$, Comm. Part. Diff. Eq., 20 (1995), 1725-1741.
doi: 10.1080/03605309508821149. |
[3] |
T. Bartsch and Z. Q. Wang, Multiple positive solutions for a nonlinear Schrödinger equation, Z. angew. Math. Phys., 51 (2000), 366-384. |
[4] |
T. Bartsch, A. Pankov and Z. Q.Wang, Nonlinear Schrödinger equations with steep potential well, Commun. Contemp. Math., 3 (2001), 549-569.
doi: 10.1142/S0219199701000494. |
[5] |
Y. Ding and K. Tanaka, Multiplicity of positive solutions of a nonlinear Schrödingerequation, Manuscripta Math., 112 (2003), 109-135.
doi: 10.1007/s00229-003-0397-x. |
[6] |
Y. Ding and A. Szulkin, Existence and number of solutions for a class of semilinearSchrödinger equation, Progr. Nonlin. Diff. Equ. Appl., 66 (2006), 221-231.
doi: 10.1007/3-7643-7401-2_15. |
[7] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, New York, 1983.
doi: 10.1007/978-3-642-61798-0. |
[8] |
A. Pankov, Periodic nonlinear Schrödinger equation with application to photoniccrystals, Milan J. Math., 73 (2005), 563-574.
doi: 10.1007/s00032-005-0047-8. |
[9] |
M. Reed and B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S), 7 (1982), 447-526. |
[10] |
Y. Sato and K. Tanaka, Sign-changingmulti-bump solutions for nonlinear Schrödinger equations withsteep potential wells, Trans. Amer. Math. Soc., 361 (2009), 6205-6253.
doi: 10.1090/S0002-9947-09-04565-6. |
[11] |
A. Szulkin and T. Weth, Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 (2009), 3802-3822.
doi: 10.1016/j.jfa.2009.09.013. |
[12] |
Z. P. Wang and H. S. Zhou, Positive solutions for nonlinear Schrödinger equations withdeepening potential well, J. Europ. Math. Soc., 11 (2009), 545-573.
doi: 10.4171/JEMS/160. |
show all references
References:
[1] |
T. Bartsch and M. Parnet, Nonlinear Schrödinger equations near an infinite potential well, arXiv:1205.1345. |
[2] |
T. Bartsch and Z. Q. Wang, Existence and multiplicity results for some superlinear ellipticequation $\mathbb{R}^N2$, Comm. Part. Diff. Eq., 20 (1995), 1725-1741.
doi: 10.1080/03605309508821149. |
[3] |
T. Bartsch and Z. Q. Wang, Multiple positive solutions for a nonlinear Schrödinger equation, Z. angew. Math. Phys., 51 (2000), 366-384. |
[4] |
T. Bartsch, A. Pankov and Z. Q.Wang, Nonlinear Schrödinger equations with steep potential well, Commun. Contemp. Math., 3 (2001), 549-569.
doi: 10.1142/S0219199701000494. |
[5] |
Y. Ding and K. Tanaka, Multiplicity of positive solutions of a nonlinear Schrödingerequation, Manuscripta Math., 112 (2003), 109-135.
doi: 10.1007/s00229-003-0397-x. |
[6] |
Y. Ding and A. Szulkin, Existence and number of solutions for a class of semilinearSchrödinger equation, Progr. Nonlin. Diff. Equ. Appl., 66 (2006), 221-231.
doi: 10.1007/3-7643-7401-2_15. |
[7] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, New York, 1983.
doi: 10.1007/978-3-642-61798-0. |
[8] |
A. Pankov, Periodic nonlinear Schrödinger equation with application to photoniccrystals, Milan J. Math., 73 (2005), 563-574.
doi: 10.1007/s00032-005-0047-8. |
[9] |
M. Reed and B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. (N.S), 7 (1982), 447-526. |
[10] |
Y. Sato and K. Tanaka, Sign-changingmulti-bump solutions for nonlinear Schrödinger equations withsteep potential wells, Trans. Amer. Math. Soc., 361 (2009), 6205-6253.
doi: 10.1090/S0002-9947-09-04565-6. |
[11] |
A. Szulkin and T. Weth, Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 (2009), 3802-3822.
doi: 10.1016/j.jfa.2009.09.013. |
[12] |
Z. P. Wang and H. S. Zhou, Positive solutions for nonlinear Schrödinger equations withdeepening potential well, J. Europ. Math. Soc., 11 (2009), 545-573.
doi: 10.4171/JEMS/160. |
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