Nagumo and Landesman-Lazer type conditions for nonlinear second order systems

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We study the existence of solutions for a nonlinear second order system of ordinary differential equations under various boundary conditions. Assuming suitable Nagumo type conditions we prove the existence of at least one solution applying the method of upper and lower solutions. Moreover, using top...

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Autor principal: Amster, P.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2007
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 0 |a Nagumo and Landesman-Lazer type conditions for nonlinear second order systems 
260 |c 2007 
270 1 0 |m Amster, P.; FCEyN - Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina; email: pamster@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a B. ALZIARY, L. CARDOULIS and J. FLECKINGER-PELLÉ, Maximum principle and existence of solutions for elliptic systems involving Schrödinger operators, rev. R. Acad. Cs. Ex. Fis. Nat. (Spain) 91(1) (1997), 47-52; DE COSTER, C., HABETS, P., Upper and lower solutions in the theory of ode boundary value problems: Classical and recent results (1997) CISM Courses and Lectures, 371. , Nonlinear Analysis and boundary value problems for ODEs, Springer 
504 |a FABRY, C.H., HABETS, P., Upper and lower solutions for second-order boundary value problems with nonlinear boundary conditions (1986) Nonlinear Analysis, 10, pp. 985-1007 
504 |a DE FIGUEIREDO, D.G., MITIDIERI, E., A maximum principle for an elliptic system and applications to semilinear problems (1986) S.I.A.M J. Math. Analysis, 17, pp. 836-849 
504 |a FLECKINGER, J., HERNANDEZ, J., DE THÉLIN, F., On maximum principles and existence of positive solutions for some cooperative elliptic systems (1995) Diff and Int Eq, 8 (1), pp. 69-85 
504 |a FRANCO, D., O'REGAN, D., Existence of solutions to second order problems with nonlinear boundary conditions (2003) Proc. of the Fourth Int. Conf. on Dynamical Systems and Diff. Equations, Discrete and Continuous Dynamical Systems, pp. 273-280 
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 GROSSINHO, M., TERSIAN, S., The dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation (2000) Nonlinear Analysis, Theory, Methods, and Applications, 41, pp. 417-431 
504 |a LANDESMAN, E., LAZER, A., Nonlinear perturbations of linear elliptic boundary value problems at resonance (1970) J. Math. Mech, 19, pp. 609-623 
504 |a LEPIN, A., SADYRBAEV, F., The Upper and Lower Functions Method for Second Order Systems (2001) Journal of Analysis and its Applications, 20 (3), pp. 739-753 
504 |a MA, T.F., Existence results for a model of nonlinear beam on elastic bearings (2000) Applied Mathematical Letters, 13, pp. 11-15 
504 |a MAWHIN, J., Topological degree methods in nonlinear boundary value problems (1979) NSF-CBMS Regional Conference in Mathematics, 40. , American Mathematical Society, Providence, RI 
504 |a MAWHIN, J., Landesman-Lazer conditions for boundary value problems: A nonlinear version of resonance (2000) Bol. de la Sociedad Española de Mat. Aplicada, 16, pp. 45-65 
504 |a NIRENBERG, L., Generalized degree and nonlinear problems (1971) Contributions to nonlinear functional analysis, pp. 1-9. , Ed. E. H. Zarantonello, Academic Press, New York 
504 |a ORTEGA, R., SÁNCHEZ, L., Periodic solutions of forced oscillators with several degrees of freedom (2002) Bull. London Math. Soc, 34, pp. 308-318 
504 |a REBELO, C., SANCHEZ, L., Existence and multiplicity for an O.D.E. with nonlinear boundary conditions (1995) Differential Equations and Dynamical Systems, 3 (4), pp. 383-396. , October 
504 |a YANG, X., Upper and lower solutions for periodic problems (2003) Appl. Math. Comput, 137 (2-3), pp. 413-422 
520 3 |a We study the existence of solutions for a nonlinear second order system of ordinary differential equations under various boundary conditions. Assuming suitable Nagumo type conditions we prove the existence of at least one solution applying the method of upper and lower solutions. Moreover, using topological degree methods we prove the existence of solutions under Landesman-Lazer type conditions. © 2006 Birkhäuser Verlag, Basel.  |l eng 
593 |a FCEyN - Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina 
593 |a Consejo Nacional de Investigaciones, Científicas y Técnicas (CONICET), Buenos Aires, Argentina 
690 1 0 |a LANDESMAN-LAZER CONDITIONS 
690 1 0 |a NAGUMO CONDITION 
690 1 0 |a NONLINEAR SYSTEMS 
690 1 0 |a TOPOLOGICAL DEGREE METHODS 
773 0 |d 2007  |g v. 13  |h pp. 699-711  |k n. 5-6  |p Nonlinear Diff. Equ. Appl.  |x 10219722  |t Nonlinear Differential Equations and Applications 
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856 4 0 |u https://doi.org/10.1007/s00030-006-4042-8  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_10219722_v13_n5-6_p699_Amster  |y Handle 
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