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Volumn 141, Issue 1, 2003, Pages 113-123

Recent progress in the theory of formal solutions for ODE and PDE

Author keywords

Borel summability; Gevrey order; Modified Nagumo norms; Multisummability; Singular perturbation

Indexed keywords

MATHEMATICAL OPERATORS; PERTURBATION TECHNIQUES; THEOREM PROVING; VECTORS;

EID: 0037457779     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00325-9     Document Type: Conference Paper
Times cited : (8)

References (28)
  • 2
    • 0012659522 scopus 로고
    • Growth estimates for the coefficients of generalized formal solutions, and representation of solutions using Laplace integrals and factorial series
    • Balser W. Growth estimates for the coefficients of generalized formal solutions, and representation of solutions using Laplace integrals and factorial series. Hiroshima Math. J. 12:1982;11-42.
    • (1982) Hiroshima Math. J. , vol.12 , pp. 11-42
    • Balser, W.1
  • 3
    • 84974185461 scopus 로고
    • Solutions of first level of meromorphic differential equations
    • Balser W. Solutions of first level of meromorphic differential equations. Proc. Edinburgh Math. Soc. 25:1982;183-207.
    • (1982) Proc. Edinburgh Math. Soc. , vol.25 , pp. 183-207
    • Balser, W.1
  • 4
    • 84972540343 scopus 로고
    • A constructive existence proof for first level formal solutions of meromorphic differential equations
    • Balser W. A constructive existence proof for first level formal solutions of meromorphic differential equations. Hiroshima Math. J. 15:1985;411-427.
    • (1985) Hiroshima Math. J. , vol.15 , pp. 411-427
    • Balser, W.1
  • 5
    • 0012701686 scopus 로고
    • A different characterization of multisummable power series
    • Balser W. A different characterization of multisummable power series. Analysis. 12:1992;57-65.
    • (1992) Analysis , vol.12 , pp. 57-65
    • Balser, W.1
  • 6
    • 0012759113 scopus 로고
    • Summation of formal power series through iterated Laplace integrals
    • Balser W. Summation of formal power series through iterated Laplace integrals. Math. Scandinavica. 70:1992;161-171.
    • (1992) Math. Scandinavica , vol.70 , pp. 161-171
    • Balser, W.1
  • 7
    • 0003223456 scopus 로고
    • From divergent power series to analytic functions
    • Springer Verlag, New York
    • W. Balser, From Divergent Power Series to Analytic Functions, Lecture Notes in Math., vol. 1582, Springer Verlag, New York, 1994.
    • (1994) Lecture Notes in Math. , vol.1582
    • Balser, W.1
  • 8
    • 0012754319 scopus 로고    scopus 로고
    • Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schäfke
    • Balser W. Divergent solutions of the heat equation: on an article of Lutz, Miyake and Schäfke. Pacific J. Math. 188:1999;53-63.
    • (1999) Pacific J. Math. , vol.188 , pp. 53-63
    • Balser, W.1
  • 10
    • 0036657387 scopus 로고    scopus 로고
    • Singular perturbation of linear systems with a regular singularity
    • Balser W., Kostov V. Singular perturbation of linear systems with a regular singularity. J. Dyn. Control Syst. 8:2002;313-322.
    • (2002) J. Dyn. Control Syst. , vol.8 , pp. 313-322
    • Balser, W.1    Kostov, V.2
  • 11
    • 0012659855 scopus 로고    scopus 로고
    • Summability of formal solutions of certain partial differential equations
    • Balser W., Miyake M. Summability of formal solutions of certain partial differential equations. Acta Sci. Math. (Szeged). 65:1999;543-551.
    • (1999) Acta Sci. Math. (Szeged) , vol.65 , pp. 543-551
    • Balser, W.1    Miyake, M.2
  • 12
    • 0037055755 scopus 로고    scopus 로고
    • Multisummability of formal solutions of singular perturbation problems
    • Balser W., Mozo-Fernandez J. Multisummability of formal solutions of singular perturbation problems. J. Differ. Equations. 183:2002;526-545.
    • (2002) J. Differ. Equations , vol.183 , pp. 526-545
    • Balser, W.1    Mozo-Fernandez, J.2
  • 13
    • 0000297561 scopus 로고
    • Multisummability of formal power series solutions of nonlinear meromorphic differential equations
    • Braaksma B.L.J. Multisummability of formal power series solutions of nonlinear meromorphic differential equations. Ann. Inst. Fourier (Grenoble). 42:1992;517-540.
    • (1992) Ann. Inst. Fourier (Grenoble) , vol.42 , pp. 517-540
    • Braaksma, B.L.J.1
  • 17
    • 0001457072 scopus 로고    scopus 로고
    • Formal power series solutions of nonlinear first order partial differential equations
    • Gérard R., Tahara H. Formal power series solutions of nonlinear first order partial differential equations. Funkcialaj Ekvacioj. 41:1998;133-166.
    • (1998) Funkcialaj Ekvacioj , vol.41 , pp. 133-166
    • Gérard, R.1    Tahara, H.2
  • 18
    • 0002926274 scopus 로고    scopus 로고
    • On the Borel summability of divergent solutions of the heat equation
    • Lutz D.A., Miyake M., Schäfke R. On the Borel summability of divergent solutions of the heat equation. Nagoya Math. J. 154:1999;1-29.
    • (1999) Nagoya Math. J. , vol.154 , pp. 1-29
    • Lutz, D.A.1    Miyake, M.2    Schäfke, R.3
  • 19
    • 0012657698 scopus 로고
    • Relations of equations of Euler, Hermite and Weber via the heat equation
    • Miyake M. Relations of equations of Euler, Hermite and Weber via the heat equation. Funkcialaj Ekvacioj. 36:1993;251-273.
    • (1993) Funkcialaj Ekvacioj , vol.36 , pp. 251-273
    • Miyake, M.1
  • 20
    • 84972493836 scopus 로고
    • Newton polygons and Gevrey indices for linear partial differential operators
    • Miyake M., Hashimoto Y. Newton polygons and Gevrey indices for linear partial differential operators. Nagoya Math. J. 128:1992;15-47.
    • (1992) Nagoya Math. J. , vol.128 , pp. 15-47
    • Miyake, M.1    Hashimoto, Y.2
  • 21
    • 0012660196 scopus 로고
    • Fredholm property for differential operators on formal Gevrey space and Toeplitz operator method
    • Miyake M., Yoshino M. Fredholm property for differential operators on formal Gevrey space and Toeplitz operator method. C.R. Acad. Bulgare de Sciences. 47:1994;21-26.
    • (1994) C.R. Acad. Bulgare de Sciences , vol.47 , pp. 21-26
    • Miyake, M.1    Yoshino, M.2
  • 22
    • 84972531415 scopus 로고
    • Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space
    • Miyake M., Yoshino M. Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space. Nagoya Math. J. 135:1994;165-196.
    • (1994) Nagoya Math. J. , vol.135 , pp. 165-196
    • Miyake, M.1    Yoshino, M.2
  • 23
    • 0001104287 scopus 로고
    • Toeplitz operators and an index theorem for differential operators on Gevrey spaces
    • Miyake M., Yoshino M. Toeplitz operators and an index theorem for differential operators on Gevrey spaces. Funkcialaj Ekvacioj. 38:1995;329-342.
    • (1995) Funkcialaj Ekvacioj , vol.38 , pp. 329-342
    • Miyake, M.1    Yoshino, M.2
  • 25
    • 0012705124 scopus 로고
    • Formal solutions with Gevrey type estimates of nonlinear partial differential equations
    • Ouchi S. Formal solutions with Gevrey type estimates of nonlinear partial differential equations. J. Math. Sci. Univ. Tokyo. 1:1994;205-237.
    • (1994) J. Math. Sci. Univ. Tokyo , vol.1 , pp. 205-237
    • Ouchi, S.1
  • 26
    • 22644448914 scopus 로고    scopus 로고
    • Singular solutions with asymptotic expansion of linear partial differential equations in the complex domain
    • Ouchi S. Singular solutions with asymptotic expansion of linear partial differential equations in the complex domain. Publ. RIMS Kyoto University. 34:1998;291-311.
    • (1998) Publ. RIMS Kyoto University , vol.34 , pp. 291-311
    • Ouchi, S.1
  • 27
    • 0000100445 scopus 로고
    • Les séries k-sommables et leurs applications
    • D. Iagolnitzer (Ed.), Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory, Springer Verlag, New York
    • J.-P. Ramis, Les séries k-sommables et leurs applications, in: D. Iagolnitzer (Ed.), Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory, vol. 126, Lecture Notes in Physics, Springer Verlag, New York, 1980, pp. 178-199.
    • (1980) Lecture Notes in Physics , vol.126 , pp. 178-199
    • Ramis, J.-P.1
  • 28
    • 0012729929 scopus 로고
    • A new proof of multisummability of formal solutions of nonlinear meromorphic differential equations
    • Ramis J.-P., Sibuya Y. A new proof of multisummability of formal solutions of nonlinear meromorphic differential equations. Ann. Inst. Fourier (Grenoble). 44:1994;811-848.
    • (1994) Ann. Inst. Fourier (Grenoble) , vol.44 , pp. 811-848
    • Ramis, J.-P.1    Sibuya, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.