메뉴 건너뛰기




Volumn 10, Issue 3, 2011, Pages 937-961

Nonautonomous continuation of bounded solutions

Author keywords

Dichotomy spectrum; Difference equation; Discretization; Exponential dichotomy; Functional differential equation; Hyperbolicity; Nonautonomous continuation; Stable manifold; Surjective implicit function theorem

Indexed keywords


EID: 79952104625     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2011.10.937     Document Type: Article
Times cited : (31)

References (35)
  • 3
    • 0010708291 scopus 로고
    • Ordinary differential equations: An introduction to nonlinear analysis
    • Walter De Gruyter, Berlin-New York
    • H. Amann, "Ordinary Differential Equations: An Introduction to Nonlinear Analysis," Studies in Mathematics 13, Walter De Gruyter, Berlin-New York, 1990.
    • (1990) Studies in Mathematics , vol.13
    • Amann, H.1
  • 5
    • 8644219736 scopus 로고    scopus 로고
    • The dichotomy spectrum for noninvertible systems of linear difference equations
    • B. Aulbach and S. Siegmund, The dichotomy spectrum for noninvertible systems of linear difference equations, Journal of Difference Equations and Applications, 7 (2001), 895-913.
    • (2001) Journal of Difference Equations and Applications , vol.7 , pp. 895-913
    • Aulbach, B.1    Siegmund, S.2
  • 6
    • 11144255492 scopus 로고    scopus 로고
    • Invertibility and the Fredholm property of difference operators
    • A. G. Baskakov, Invertibility and the Fredholm property of difference operators, Mathematical Notes, 67 (2000), 690-698.
    • (2000) Mathematical Notes , vol.67 , pp. 690-698
    • Baskakov, A.G.1
  • 7
    • 0000082530 scopus 로고
    • Dichotomy, discrete Bohl exponents, and spectrum of block weighted shifts
    • A. Ben-Artzi and I. Gohberg, Dichotomy, discrete Bohl exponents, and spectrum of block weighted shifts, Integral Equations and Operator Theory, 14 (1991), 613-677.
    • (1991) Integral Equations and Operator Theory , vol.14 , pp. 613-677
    • Ben-Artzi, A.1    Gohberg, I.2
  • 8
    • 82155179626 scopus 로고    scopus 로고
    • Counting uniformly attracting solutions of nonautonomous differential equations
    • A. Berger, Counting uniformly attracting solutions of nonautonomous differential equations, Discrete and Continuous Dynamical Systems (Series S), 1 (2008), 15-25.
    • (2008) Discrete and Continuous Dynamical Systems (Series S) , vol.1 , pp. 15-25
    • Berger, A.1
  • 9
    • 42949102956 scopus 로고    scopus 로고
    • Uniformly attracting solutions of nonautonomous differential equations
    • A. Berger and S. Siegmund, Uniformly attracting solutions of nonautonomous differential equations, Nonlinear Analysis (TMA), 68 (2008), 3789-3811.
    • (2008) Nonlinear Analysis (TMA) , vol.68 , pp. 3789-3811
    • Berger, A.1    Siegmund, S.2
  • 10
  • 11
    • 0042031284 scopus 로고    scopus 로고
    • Safety criteria for aperiodically forced systems
    • Z. Bishnani and R. S. Mackay, Safety criteria for aperiodically forced systems, Dynamical Systems, 18 (2003), 107-129.
    • (2003) Dynamical Systems , vol.18 , pp. 107-129
    • Bishnani, Z.1    Mackay, R.S.2
  • 12
    • 77957809348 scopus 로고    scopus 로고
    • Solutions of linear and nonlinear difference equations bounded on the whole line
    • O. Boichuk, Solutions of linear and nonlinear difference equations bounded on the whole line, Nonlinear Oscillations, 4 (2001), 16-27.
    • (2001) Nonlinear Oscillations , vol.4 , pp. 16-27
    • Boichuk, O.1
  • 14
    • 54349099620 scopus 로고    scopus 로고
    • Ordinary differential equations with applications
    • 2nd edition, Springer, Berlin etc
    • C. Chicone, "Ordinary Differential Equations with Applications," 2nd edition, Texts in Applied Mathematics 34, Springer, Berlin etc., 2006.
    • (2006) Texts in Applied Mathematics , vol.34
    • Chicone, C.1
  • 15
    • 0003327379 scopus 로고    scopus 로고
    • Evolution semigroups in dynamical systems and differential equations
    • AMS, Providence RI
    • C. Chicone and Y. Latushkin, "Evolution Semigroups in Dynamical Systems and Differential Equations," Mathematical Surveys and Monographs 70, AMS, Providence RI, 1999.
    • (1999) Mathematical Surveys and Monographs , vol.70
    • Chicone, C.1    Latushkin, Y.2
  • 16
    • 0002709196 scopus 로고
    • Dichotomies in stability theory
    • Springer, Berlin etc
    • W. A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Math. 629, Springer, Berlin etc., 1978.
    • (1978) Lecture Notes in Math. , vol.629
    • Coppel, W.A.1
  • 17
    • 0035423896 scopus 로고    scopus 로고
    • The converse of the theorem on stability by the first approximation for difference equations
    • I. Gyóri and M. Pituk, The converse of the theorem on stability by the first approximation for difference equations, Nonlinear Analysis (TMA), 47 (2001), 4635-4640.
    • (2001) Nonlinear Analysis (TMA) , vol.47 , pp. 4635-4640
    • Gyóri, I.1    Pituk, M.2
  • 18
    • 4544272717 scopus 로고    scopus 로고
    • Hyperbolic trajectories of time discretizations
    • A. Hagen, Hyperbolic trajectories of time discretizations, Nonlinear Analysis (TMA), 59 (2004), 121-132.
    • (2004) Nonlinear Analysis (TMA) , vol.59 , pp. 121-132
    • Hagen, A.1
  • 19
    • 0003324723 scopus 로고
    • Introduction to functional differential equations
    • Springer, Berlin etc
    • J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations," Applied Mathematical Sciences 99, Springer, Berlin etc., 1993.
    • (1993) Applied Mathematical Sciences , vol.99
    • Hale, J.K.1    Verduyn Lunel, S.M.2
  • 20
    • 1342307277 scopus 로고    scopus 로고
    • On perturbations of delay-differential equations with periodic orbits
    • J. K. Hale and M. Weedermann, On perturbations of delay-differential equations with periodic orbits, Journal of Differential Equations, 197 (2004), 219-246.
    • (2004) Journal of Differential Equations , vol.197 , pp. 219-246
    • Hale, J.K.1    Weedermann, M.2
  • 21
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer, Berlin etc
    • D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Math. 840, Springer, Berlin etc., 1981.
    • (1981) Lecture Notes in Math. , vol.840
    • Henry, D.1
  • 23
    • 70549114661 scopus 로고
    • Explicit and ε for the implicit function theorem
    • J. M. Holtzman, Explicit " and ε for the implicit function theorem, SIAM Review, 12 (1970), 284-286.
    • (1970) SIAM Review , vol.12 , pp. 284-286
    • Holtzman, J.M.1
  • 25
    • 0000480907 scopus 로고
    • Bifurcation of maps and applications
    • North-Holland, Amsterdam
    • G. Iooss, "Bifurcation of Maps and Applications," Mathematics Studies 36, North-Holland, Amsterdam, 1979.
    • (1979) Mathematics Studies , vol.36
    • Iooss, G.1
  • 26
    • 0041377838 scopus 로고    scopus 로고
    • Existence and computation of hyperbolic trajectories of aperiodically time dependent vector ffelds and their approximations
    • N. Ju, D. Small and S. Wiggins, Existence and computation of hyperbolic trajectories of aperiodically time dependent vector ffelds and their approximations, International Journal of Bifurcation and Chaos, 13 (2003), 1449-1457.
    • (2003) International Journal of Bifurcation and Chaos , vol.13 , pp. 1449-1457
    • Ju, N.1    Small, D.2    Wiggins, S.3
  • 28
    • 9244262277 scopus 로고    scopus 로고
    • Bifurcation theory: An introduction with applications to PDEs
    • Springer, New York
    • H. Kielhöfer, "Bifurcation Theory: An Introduction with Applications to PDEs," Applied Mathematical Sciences 156, Springer, New York, 2004.
    • (2004) Applied Mathematical Sciences , vol.156
    • Kielhöfer, H.1
  • 30
    • 0004480637 scopus 로고
    • Real and functional analysis
    • Springer, Berlin etc
    • S. Lang, "Real and Functional Analysis," Graduate Texts in Mathematics 142, Springer, Berlin etc., 1993.
    • (1993) Graduate Texts in Mathematics , vol.142
    • Lang, S.1
  • 31
    • 0031534009 scopus 로고    scopus 로고
    • An infinite-dimensional extension of a Poincarffe result concerning the continuation of periodic orbits
    • P. Perfetti, An infinite-dimensional extension of a Poincarffe result concerning the continuation of periodic orbits, Discrete and Continuous Dynamical Systems, 3 (1997), 401-418.
    • (1997) Discrete and Continuous Dynamical Systems , vol.3 , pp. 401-418
    • Perfetti, P.1
  • 33
    • 12244272462 scopus 로고    scopus 로고
    • Taylor approximation of invariant fiber bundles
    • C. Pötzsche and M. Rasmussen, Taylor approximation of invariant fiber bundles, Nonlinear Analysis (TMA), 60 (2005), 1303-1330.
    • (2005) Nonlinear Analysis (TMA) , vol.60 , pp. 1303-1330
    • Pötzsche, C.1    Rasmussen, M.2
  • 34
    • 0242689013 scopus 로고    scopus 로고
    • Dynamics of evolutionary equations
    • Springer, Berlin etc
    • G. R. Sell and Y. You, "Dynamics of Evolutionary Equations," Applied Mathematical Sciences 143, Springer, Berlin etc., 2002.
    • (2002) Applied Mathematical Sciences , vol.143
    • Sell, G.R.1    You, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.