Artículo
Amster, P. "Solvability of weakly coupled second order systems with rapidly oscillating nonlinearities" (2012) Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis. 19(5):535-543
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Abstract:
We study the existence of periodic solutions for a nonlinear system of second order ordinary differential equations. Assuming suitable conditions, we prove the existence of at least one solution applying topological degree methods. Instead of a Nirenberg type condition, we shall assume that each coordinate of the nonlinearity satisfies a one-side Landesman-Lazer type condition, but it might present rapid oscillations on the other side. Copyright © 2012 Watam Press.
Registro:
| Documento: | Artículo |
| Título: | Solvability of weakly coupled second order systems with rapidly oscillating nonlinearities |
| Autor: | Amster, P. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina |
| Palabras clave: | Landesman-lazer conditions; Nonlinear second order systems; Periodic solutions; Rapid oscillations; Topological degree methods |
| Año: | 2012 |
| Volumen: | 19 |
| Número: | 5 |
| Página de inicio: | 535 |
| Página de fin: | 543 |
| Título revista: | Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis |
| Título revista abreviado: | Dyn. Contin. Discrete Impulsive Syst. Ser. A Math. Anal. |
| ISSN: | 12013390 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12013390_v19_n5_p535_Amster |
Referencias:
- Amster, P., De Napoli, P., Landesman-Lazer type conditions for a system of p-Laplacian like operators (2007) Journal of Mathematical Analysis and Applications, 326 (2), pp. 1236-1243. , DOI 10.1016/j.jmaa.2006.04.001, PII S0022247X06003477
- Cesari, L., Kannan, R., Qualitative study of a class of nonlinear boundary value problems at resonance (1985) Journal of Differential Equations, 56, pp. 63-81
- Fucik, S., (1980) Solvability of Nonlinear Equations and Boundary Value Problems, , Chapter 24, D. Reidel, Holland
- Iannacci, R., Nkashama, M., Ward, J.R., Nonlinear second order elliptic partial differential equations at resonance (1989) Trans. Amer. Math. Soc., 311 (2), pp. 711-726
- Kannan, R., Nagle, K., Forced oscillations with rapidly vanishing nonlinearities (1991) Proc. of the American Math. Soc., 111 (2), pp. 385-393
- Kannan, R., Ortega, R., Periodic solutions of pendulum-type equations (1985) Journal of Differential Equations, 59, pp. 123-144
- Landesman, E., Lazer, A., Nonlinear perturbations of linear elliptic boundary value problems at resonance (1970) J. Math. Mech., 19, pp. 609-623
- Mawhin, J., (1979) Topological Degree Methods in Nonlinear Boundary Value Problems, NSF-CBMS Regional Conference in Mathematics No. 40, , American Mathematical Society, Providence, RI
- 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
- Nirenberg, L., (1971) Generalized Degree and Nonlinear Problems, Contributions to Nonlinear Functional Analysis, pp. 1-9. , E. H. Zarantonello, Academic Press New York
- Ortega, R., Ward Jr., J.R., A semilinear eliptic system with vanishing nonlinearities (2002) Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, pp. 688-693
- Ruiz, D., Ward, J.R., Some notes on periodic systems with linear part at resonance (2004) Discrete and Continuous Dynamical Systems, 11 (2-3), pp. 337-350
Citas:
---------- APA ----------
(2012) . Solvability of weakly coupled second order systems with rapidly oscillating nonlinearities. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 19(5), 535-543.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12013390_v19_n5_p535_Amster [ ]
---------- CHICAGO ----------
Amster, P. "Solvability of weakly coupled second order systems with rapidly oscillating nonlinearities" . Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis 19, no. 5 (2012) : 535-543.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12013390_v19_n5_p535_Amster [ ]
---------- MLA ----------
Amster, P. "Solvability of weakly coupled second order systems with rapidly oscillating nonlinearities" . Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, vol. 19, no. 5, 2012, pp. 535-543.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12013390_v19_n5_p535_Amster [ ]
---------- VANCOUVER ----------
Amster, P. Solvability of weakly coupled second order systems with rapidly oscillating nonlinearities. Dyn. Contin. Discrete Impulsive Syst. Ser. A Math. Anal. 2012;19(5):535-543.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12013390_v19_n5_p535_Amster [ ]
