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Abstract:

We study the existence of solutions for a periodic fourth order problem. We prove an associated uniform antimaximum principle and develop a method of upper and lower solutions in reversed order. Furthermore, by the quasilinearization method we construct an iterative sequence that converges quadratically to a solution.

Registro:

Documento: Artículo
Título:An application of the antimaximum principle for a fourth order periodic problem
Autor:Amster, P.; De Nápoli, P.
Filiación:Departamento de Matemática, FCEyN, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina
Palabras clave:Antimaximum principle; Fourth order periodic problems; Quasilinearization method; Upper and lower solutions
Año:2006
Página de inicio:1
Página de fin:11
Título revista:Electronic Journal of Qualitative Theory of Differential Equations
Título revista abreviado:Electron. J. Qual. Theor. Differ. Equ.
ISSN:14173875
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14173875_v_n_p1_Amster

Referencias:

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  • Cabada, A., Habets, P., Lois, S., Monotone method of the Neumann problem with lower and upper solutions in the reverse order (2001) Appl. Math. Comput., 117, pp. 1-14
  • Cabada, A., Sanchez, L., A positive operator approach to the Neumann problem for second order ordinary differential equation (1996) J. Math. Anal. Appl., 204, pp. 774-785
  • Cabada, A., Nieto, J.J., Quasilinearization and rate of convergence for higher-order nonlinear periodic boundary-value problems (2001) J. Optim. Theory Appl., 108 (1), pp. 97-107
  • Clément, Ph., Peletier, L.A., An anti maximum principle for second order elliptic, problems (1979) J. Diff. Equations, 34 (2), pp. 218-229
  • De Coster, C., Habets, P., An overview of the method of lower and upper solutions for ODE (2001) Progress in Nonlinear Differential Equations and Their Applications, 43, pp. 3-22. , "Nonlinear analysis and its Applications to Differential Equations" (M.R. Grossinho, M. Ramos, C. Rebelo et L. Sanchez eds), Birkhauser, Boston
  • Gossez, J.P., Some remarks on the antimaximum principle (1998) Revista de la Unión Matemática Argentina, 41 (1), pp. 79-84
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  • Lakshmikantham, V., Nieto, J.J., Generalized quasilinearization for nonlinear first order ordinary differential equations (1995) Nonlinear Times Digest, 2 (1), pp. 1-9
  • Lakshmikantham, V., Shahzad, N., Nieto, J.J., Methods of generalized quasilinearization for periodic boundary value problems (1996) Nonlinear Anal., 27 (2), pp. 143-151
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  • Lakshmikantham, V., An extension of the method of quasilinearization (1994) J. Optim. Theory Appl., 82, pp. 315-321
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Citas:

---------- APA ----------
Amster, P. & De Nápoli, P. (2006) . An application of the antimaximum principle for a fourth order periodic problem. Electronic Journal of Qualitative Theory of Differential Equations, 1-11.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14173875_v_n_p1_Amster [ ]
---------- CHICAGO ----------
Amster, P., De Nápoli, P. "An application of the antimaximum principle for a fourth order periodic problem" . Electronic Journal of Qualitative Theory of Differential Equations (2006) : 1-11.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14173875_v_n_p1_Amster [ ]
---------- MLA ----------
Amster, P., De Nápoli, P. "An application of the antimaximum principle for a fourth order periodic problem" . Electronic Journal of Qualitative Theory of Differential Equations, 2006, pp. 1-11.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14173875_v_n_p1_Amster [ ]
---------- VANCOUVER ----------
Amster, P., De Nápoli, P. An application of the antimaximum principle for a fourth order periodic problem. Electron. J. Qual. Theor. Differ. Equ. 2006:1-11.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14173875_v_n_p1_Amster [ ]