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Abstract:

It is established that, under certain conditions, the Dirichlet problem on a bounded interval for the Painlevé II equation is uniquely solvable and solutions are constructed in an iterative manner. Moreover, conditions for the existence of periodic solutions are set down. © 2002 Elsevier Science.

Registro:

Documento: Artículo
Título:Dirichlet and periodic-type boundary value problems for Painlevé II
Autor:Mariani, M.C.; Amster, P.; Rogers, C.
Filiación:Departamento De Matemática, Facultad De Ciencias Exactas Y Naturales, Universidad De Buenos Aires, Buenos Aires, Argentina
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
Año:2002
Volumen:265
Número:1
Página de inicio:1
Página de fin:11
DOI: http://dx.doi.org/10.1006/jmaa.2001.7675
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v265_n1_p1_Mariani.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v265_n1_p1_Mariani

Referencias:

  • Painlevé, P., Sur les équations différentielles du second ordre et d'ordre supérieur dont l'intégrale générale est uniforme (1902) Acta Math, 25, pp. 1-86
  • Ablowitz, M.J., Segur, H., Exact linearization of a Painlevé transcendent (1977) Phys. Rev. Lett, 38, pp. 1103-1106
  • Giannini, J.A., Joseph, R.I., The role of the second Painlevé transcendent in nonlinear optics (1989) Phys. Lett. A, 141, pp. 417-419
  • Bass, L., Electrical structures of interfaces in steady electrolysis (1964) Trans. Faraday Soc, 60, pp. 1656-1663
  • Richard Leuchtag, H., A family of differential equations arising from multi-ion electro-diffusion (1981) J. Math. Phys, 22, pp. 1317-1320
  • Thompson, H.B., Existence of solutions for a two point boundary value problem arising in electro-diffusion (1988) Acta Math. Sci, 8, pp. 373-387
  • Kudryashov, N.A., The second Painlevé equation as a model for the electric field in a semi-conductor (1997) Phys. Lett. A, 233, pp. 397-400
  • Rogers, C., Bassom, A.P., Schief, W.K., On a Painlevé II model in steady electrolysis: Application of a Bäcklund transformation (1999) J. Math. Anal. Appl, 240, pp. 367-381
  • Hastings, S.P., A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation (1980) Arch. Rational Mech. Anal, 73, pp. 31-51
  • de Boer, P.C.T., Ludford, G.S.S., Spherical electric probe in a continuum gas (1975) Plasma Phys, 17, pp. 29-43
  • Holmes, P., Spence, D., On a Painlevé-type problem (1989) Quart. J. Mech. Appl. Math, 37, pp. 525-538
  • Thompson, H.B., Existence for two-point boundary value problems in two ion electro-diffusion (1994) J. Math. Anal. Appl, 184, pp. 82-99

Citas:

---------- APA ----------
Mariani, M.C., Amster, P. & Rogers, C. (2002) . Dirichlet and periodic-type boundary value problems for Painlevé II. Journal of Mathematical Analysis and Applications, 265(1), 1-11.
http://dx.doi.org/10.1006/jmaa.2001.7675
---------- CHICAGO ----------
Mariani, M.C., Amster, P., Rogers, C. "Dirichlet and periodic-type boundary value problems for Painlevé II" . Journal of Mathematical Analysis and Applications 265, no. 1 (2002) : 1-11.
http://dx.doi.org/10.1006/jmaa.2001.7675
---------- MLA ----------
Mariani, M.C., Amster, P., Rogers, C. "Dirichlet and periodic-type boundary value problems for Painlevé II" . Journal of Mathematical Analysis and Applications, vol. 265, no. 1, 2002, pp. 1-11.
http://dx.doi.org/10.1006/jmaa.2001.7675
---------- VANCOUVER ----------
Mariani, M.C., Amster, P., Rogers, C. Dirichlet and periodic-type boundary value problems for Painlevé II. J. Math. Anal. Appl. 2002;265(1):1-11.
http://dx.doi.org/10.1006/jmaa.2001.7675