메뉴 건너뛰기




Volumn 13, Issue 6, 2012, Pages 2755-2766

Fractional Schrödinger equations with potential and optimal controls

Author keywords

Existence; Fractional Schr dinger equations; Local stability and attractivity; Mild solutions; Optimal controls; Potential

Indexed keywords

ATTRACTIVITY; DINGER EQUATION; EXISTENCE; MILD SOLUTION; OPTIMAL CONTROLS; POTENTIAL;

EID: 84861937080     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2012.04.004     Document Type: Article
Times cited : (75)

References (38)
  • 2
    • 10844227674 scopus 로고    scopus 로고
    • Courant Lecture Notes in Mathematics American Mathematical Society Providence, RI New York University, Courant Institute of Mathematical Sciences, New York
    • T. Cazenave Semilinear Schrödinger Equations Courant Lecture Notes in Mathematics vol. 10 2003 American Mathematical Society Providence, RI New York University, Courant Institute of Mathematical Sciences, New York
    • (2003) Semilinear Schrödinger Equations , vol.10
    • Cazenave, T.1
  • 3
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • T. Cazenave, and P.-L. Lions Orbital stability of standing waves for some nonlinear Schrödinger equations Comm. Math. Phys. 85 1982 549 561
    • (1982) Comm. Math. Phys. , vol.85 , pp. 549-561
    • Cazenave, T.1    Lions, P.-L.2
  • 4
    • 0039683992 scopus 로고
    • Stable solutions of the logarithmic Schrödinger equation
    • T. Cazenave Stable solutions of the logarithmic Schrödinger equation Nonlinear Anal.: TMA 7 1983 1127 1140
    • (1983) Nonlinear Anal.: TMA , vol.7 , pp. 1127-1140
    • Cazenave, T.1
  • 5
    • 0001613187 scopus 로고
    • Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
    • A. Floer, and A. Weinstein Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential J. Funct. Anal. 69 1986 397 408
    • (1986) J. Funct. Anal. , vol.69 , pp. 397-408
    • Floer, A.1    Weinstein, A.2
  • 6
    • 11744356372 scopus 로고
    • Orbital stability of solitary waves for the nonlinear derivative Schrödinger equation
    • B.L. Guo, and Y.P. Wu Orbital stability of solitary waves for the nonlinear derivative Schrödinger equation J. Differential Equations 123 1995 35 55
    • (1995) J. Differential Equations , vol.123 , pp. 35-55
    • Guo, B.L.1    Wu, Y.P.2
  • 7
    • 0035595894 scopus 로고    scopus 로고
    • Stabilization of solutions to nonlinear Schrödinger equations
    • S. Cuccagna Stabilization of solutions to nonlinear Schrödinger equations Comm. Pure Appl. Math. 54 2001 1110 1145
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 1110-1145
    • Cuccagna, S.1
  • 8
    • 0038349584 scopus 로고
    • Asymptotic dynamics of nonlinear Schrödinger equations with many bound states
    • T.-P. Tsai Asymptotic dynamics of nonlinear Schrödinger equations with many bound states J. Differential Equations 192 1995 225 282
    • (1995) J. Differential Equations , vol.192 , pp. 225-282
    • Tsai, T.-P.1
  • 9
    • 0347495345 scopus 로고    scopus 로고
    • On asymptotic stability of solitary waves for nonlinear Schrödinger equations
    • V.S. Buslaev, and C. Sulem On asymptotic stability of solitary waves for nonlinear Schrödinger equations Ann. Inst. Henri Poincare (C) Non Linear Anal. 20 2003 419 475
    • (2003) Ann. Inst. Henri Poincare (C) Non Linear Anal. , vol.20 , pp. 419-475
    • Buslaev, V.S.1    Sulem, C.2
  • 11
    • 79958013537 scopus 로고    scopus 로고
    • Singular solutions of the subcritical nonlinear Schrödinger equation
    • G. Fibich Singular solutions of the subcritical nonlinear Schrödinger equation Physica D: Nonlinear Phenom. 240 2011 1119 1122
    • (2011) Physica D: Nonlinear Phenom. , vol.240 , pp. 1119-1122
    • Fibich, G.1
  • 12
    • 60549106690 scopus 로고    scopus 로고
    • On fractional Schrödinger equation in α-dimensional fractional space
    • R. Eid, S.I. Muslih, D. Baleanu, and E. Rabei On fractional Schrödinger equation in α-dimensional fractional space Nonlinear Anal.: RWA 10 2009 1299 1304
    • (2009) Nonlinear Anal.: RWA , vol.10 , pp. 1299-1304
    • Eid, R.1    Muslih, S.I.2    Baleanu, D.3    Rabei, E.4
  • 14
    • 0035877236 scopus 로고    scopus 로고
    • On the optimal control problem for linear Schrödinger equation
    • B. Yildiz, and M. Subaşi On the optimal control problem for linear Schrödinger equation Appl. Math. Comput. 121 2001 373 381
    • (2001) Appl. Math. Comput. , vol.121 , pp. 373-381
    • Yildiz, B.1    Subaşi, M.2
  • 15
    • 0037056193 scopus 로고    scopus 로고
    • An optimal control problem governed by the potential of a linear Schrödinger equation
    • M. Subaşi An optimal control problem governed by the potential of a linear Schrödinger equation Appl. Math. Comput. 131 2002 95 106
    • (2002) Appl. Math. Comput. , vol.131 , pp. 95-106
    • Subaşi, M.1
  • 16
    • 23644461902 scopus 로고    scopus 로고
    • Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control
    • L. Baudouin, O. Kavian, and J.-P. Puel Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control J. Differential Equations 216 2005 188 222
    • (2005) J. Differential Equations , vol.216 , pp. 188-222
    • Baudouin, L.1    Kavian, O.2    Puel, J.-P.3
  • 17
    • 41949123114 scopus 로고    scopus 로고
    • Constructive solution of a bilinear optimal control problem for a Schrödinger equation
    • L. Baudouin, and J. Salomon Constructive solution of a bilinear optimal control problem for a Schrödinger equation Systems Control Lett. 57 2008 453 464
    • (2008) Systems Control Lett. , vol.57 , pp. 453-464
    • Baudouin, L.1    Salomon, J.2
  • 18
    • 77953230857 scopus 로고    scopus 로고
    • On the optimal control problem for Schrödinger equation with complex potential
    • H. Yetişkin, and M. Subaşi On the optimal control problem for Schrödinger equation with complex potential Appl. Math. Comput. 216 2010 1896 1902
    • (2010) Appl. Math. Comput. , vol.216 , pp. 1896-1902
    • Yetişkin, H.1    Subaşi, M.2
  • 25
    • 77949264980 scopus 로고    scopus 로고
    • A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
    • R.P. Agarwal, M. Benchohra, and S. Hamani A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions Acta. Appl. Math. 109 2010 973 1033
    • (2010) Acta. Appl. Math. , vol.109 , pp. 973-1033
    • Agarwal, R.P.1    Benchohra, M.2    Hamani, S.3
  • 26
    • 67650110018 scopus 로고    scopus 로고
    • A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative
    • Article ID 981728
    • R.P. Agarwal, M. Belmekki, and M. Benchohra A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative Adv. Differential Equations 2009 2009 47 Article ID 981728
    • (2009) Adv. Differential Equations , vol.2009 , pp. 47
    • Agarwal, R.P.1    Belmekki, M.2    Benchohra, M.3
  • 27
    • 80052816299 scopus 로고    scopus 로고
    • Global attractivity for nonlinear fractional differential equations
    • F. Chen, J.J. Nieto, and Y. Zhou Global attractivity for nonlinear fractional differential equations Nonlinear Anal.: RWA 13 2012 287 298
    • (2012) Nonlinear Anal.: RWA , vol.13 , pp. 287-298
    • Chen, F.1    Nieto, J.J.2    Zhou, Y.3
  • 28
    • 80054946851 scopus 로고    scopus 로고
    • A study of nonlinear Langevin equation involving two fractional orders in different intervals
    • B. Ahmad, J.J. Nieto, A. Alsaedi, and M. El-Shahed A study of nonlinear Langevin equation involving two fractional orders in different intervals Nonlinear Anal.: RWA 13 2012 599 606
    • (2012) Nonlinear Anal.: RWA , vol.13 , pp. 599-606
    • Ahmad, B.1    Nieto, J.J.2    Alsaedi, A.3    El-Shahed, M.4
  • 29
    • 80051576826 scopus 로고    scopus 로고
    • Analysis of nonlinear fractional control systems in Banach spaces
    • J. Wang, and Y. Zhou Analysis of nonlinear fractional control systems in Banach spaces Nonlinear Anal.: TMA 74 2011 5929 5942
    • (2011) Nonlinear Anal.: TMA , vol.74 , pp. 5929-5942
    • Wang, J.1    Zhou, Y.2
  • 30
    • 77958009389 scopus 로고    scopus 로고
    • A class of fractional evolution equations and optimal controls
    • J. Wang, and Y. Zhou A class of fractional evolution equations and optimal controls Nonlinear Anal.: RWA 12 2011 262 272
    • (2011) Nonlinear Anal.: RWA , vol.12 , pp. 262-272
    • Wang, J.1    Zhou, Y.2
  • 31
    • 80052035803 scopus 로고    scopus 로고
    • Existence and controllability results for fractional semilinear differential inclusions
    • J. Wang, and Y. Zhou Existence and controllability results for fractional semilinear differential inclusions Nonlinear Anal.: RWA 12 2011 3642 3653
    • (2011) Nonlinear Anal.: RWA , vol.12 , pp. 3642-3653
    • Wang, J.1    Zhou, Y.2
  • 32
    • 84855519663 scopus 로고    scopus 로고
    • On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite delay
    • J. Wang, Y. Zhou, and M. Medved On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite delay J. Optim. Theory Appl. 152 2012 31 50
    • (2012) J. Optim. Theory Appl. , vol.152 , pp. 31-50
    • Wang, J.1    Zhou, Y.2    Medved, M.3
  • 33
    • 84862777911 scopus 로고    scopus 로고
    • Optimal feedback control for semilinear fractional evolution equations in Banach spaces
    • J. Wang, Y. Zhou, and W. Wei Optimal feedback control for semilinear fractional evolution equations in Banach spaces Systems Control Lett. 61 2012 472 476
    • (2012) Systems Control Lett. , vol.61 , pp. 472-476
    • Wang, J.1    Zhou, Y.2    Wei, W.3
  • 34
    • 77955515765 scopus 로고    scopus 로고
    • Nonlocal Cauchy problem for fractional evolution equations
    • Y. Zhou, and F. Jiao Nonlocal Cauchy problem for fractional evolution equations Nonlinear Anal.: RWA 11 2010 4465 4475
    • (2010) Nonlinear Anal.: RWA , vol.11 , pp. 4465-4475
    • Zhou, Y.1    Jiao, F.2
  • 35
    • 74149093181 scopus 로고    scopus 로고
    • Existence of mild solutions for fractional neutral evolution equations
    • Y. Zhou, and F. Jiao Existence of mild solutions for fractional neutral evolution equations Comput. Math. Appl. 59 2010 1063 1077
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1063-1077
    • Zhou, Y.1    Jiao, F.2
  • 38
    • 33845882236 scopus 로고    scopus 로고
    • A generalized Gronwall inequality and its application to a fractional differential equation
    • H. Ye, J. Gao, and Y. Ding A generalized Gronwall inequality and its application to a fractional differential equation J. Math. Anal. Appl. 328 2007 1075 1081
    • (2007) J. Math. Anal. Appl. , vol.328 , pp. 1075-1081
    • Ye, H.1    Gao, J.2    Ding, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.