An application of the antimaximum principle for a fourth order periodic problem

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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 quadratic...

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Detalles Bibliográficos
Autor principal: Amster, P.
Otros Autores: De Nápoli, P.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2006
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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100 1 |a Amster, P. 
245 1 3 |a An application of the antimaximum principle for a fourth order periodic problem 
260 |c 2006 
270 1 0 |m Amster, P.; Departamento de Matemática, FCEyN, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina; email: pamster@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Bellman, R., Kalaba, R., (1965) Quasilinearisation and Nonlinear Boundary Value Problems, , American Elsevier, New York 
504 |a Cherpion, M., De Coster, C., Habets, P., A constructive monotone iterative method for second order BVP in the presence of lower and upper solutions (2001) Appl. Math. Comput., 123, pp. 75-91 
504 |a 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 
504 |a 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 
504 |a 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 
504 |a Clément, Ph., Peletier, L.A., An anti maximum principle for second order elliptic, problems (1979) J. Diff. Equations, 34 (2), pp. 218-229 
504 |a 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 
504 |a Gossez, J.P., Some remarks on the antimaximum principle (1998) Revista de la Unión Matemática Argentina, 41 (1), pp. 79-84 
504 |a Grossinho, M., Minhós, F., Existence results for some third order separated boundary value problems (2001) Nonlinear Analysis, 47, pp. 2407-2418 
504 |a Grossinho, M., Ma, T.F., Symmetric equilibria for a beam with a nonlinear elastic foundation (1994) Portugaliae Mathematica, 51, pp. 375-393 
504 |a Jüngel, A., Quasi-hydrodynamic semiconductor equations (2001) Birkhäuser 
504 |a Khan, R., Existence and approximation of solutions of second order non-linear Neumann problems (2005) Electronic Journal of Differential Equations, 2005 (3), pp. 1-10 
504 |a Kosmatov, N., Countably many solutions of a fourth order boundary value problem (2004) E. J. Qualitative Theory of Diff. Equ., (12), pp. 1-15 
504 |a Lakshmikantham, V., Nieto, J.J., Generalized quasilinearization for nonlinear first order ordinary differential equations (1995) Nonlinear Times Digest, 2 (1), pp. 1-9 
504 |a Lakshmikantham, V., Shahzad, N., Nieto, J.J., Methods of generalized quasilinearization for periodic boundary value problems (1996) Nonlinear Anal., 27 (2), pp. 143-151 
504 |a Lakshmikantham, V., Vatsala, A.S., Generalized quasilinearization for nonlinear problems (1998) Mathematics and Its Applications, 440, , Kluwer Academic Publishers, Dordrecht 
504 |a Leuchtag, R., Family of differential equations arising from multi-ion electrodiffussion (1981) J. Math. Phys., 22 (6), pp. 1317-1320 
504 |a Nieto, J.J., Quadratic approximation of solutions for ordinary differential equations (1997) Bull. Austral. Math. Soc., 55 (1), pp. 161-168 
504 |a Lakshmikantham, V., An extension of the method of quasilinearization (1994) J. Optim. Theory Appl., 82, pp. 315-321 
504 |a Lakshmikantham, V., Further improvement of generalized quasilinearization (1996) Nonlinear Analysis, 27, pp. 315-321 
504 |a Yang, B., Positive solutions for a fourth order boundary value problem (2005) E. J. Qualitative Theory of Diff. Equ., (3), pp. 1-17 
520 3 |a 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.  |l eng 
593 |a Departamento de Matemática, FCEyN, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina 
690 1 0 |a ANTIMAXIMUM PRINCIPLE 
690 1 0 |a FOURTH ORDER PERIODIC PROBLEMS 
690 1 0 |a QUASILINEARIZATION METHOD 
690 1 0 |a UPPER AND LOWER SOLUTIONS 
700 1 |a De Nápoli, P. 
773 0 |d 2006  |h pp. 1-11  |p Electron. J. Qual. Theor. Differ. Equ.  |x 14173875  |w (AR-BaUEN)CENRE-4554  |t Electronic Journal of Qualitative Theory of Differential Equations 
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999 |c 68165 

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