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Abstract:

We study the existence of periodic solutions for a nonlinear second order system of ordinary differential equations of p-Laplacian type. Assuming suitable Nagumo and Landesman-Lazer type conditions we prove the existence of at least one solution applying topological degree methods. We extend a celebrated result by Nirenberg for resonant systems. © 2006 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Landesman-Lazer type conditions for a system of p-Laplacian like operators
Autor:Amster, P.; De Nápoli, P.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
Palabras clave:Landesman-Lazer conditions; p-Laplacian systems
Año:2007
Volumen:326
Número:2
Página de inicio:1236
Página de fin:1243
DOI: http://dx.doi.org/10.1016/j.jmaa.2006.04.001
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_v326_n2_p1236_Amster.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v326_n2_p1236_Amster

Referencias:

  • Cabada, A., Pouso, R.L., Existence result for the problem (φ{symbol} (u′))′ = f (t, u, u′) with periodic and Neumann boundary conditions (1997) Nonlinear Anal., 30 (3), pp. 1733-1742. , Proc. of the Second World Congress of Nonlinear Analysts
  • Franco, D., O'Regan, D., Existence of solutions to second order problems with nonlinear boundary conditions (2003) Discrete Contin. Dyn. Syst., pp. 273-280. , Proc. of the Fourth Int. Conf. on Dynamical Systems and Diff. Equations
  • Ge, W.G., Ren, J.L., An extension of Mawhin's continuation theorem and its application to boundary value problems with a p-Laplacian (2004) Nonlinear Anal., 58 (4), pp. 477-488
  • Landesman, E., Lazer, A., Nonlinear perturbations of linear elliptic boundary value problems at resonance (1970) J. Math. Mech., 19, pp. 609-623
  • Manásevich, R., Mawhin, J., Periodic solutions for nonlinear systems with p-Laplacian like operators (1998) J. Differential Equations, 145 (2), pp. 367-393
  • Mawhin, J., Topological Degree Methods in Nonlinear Boundary Value Problems (1979) NSF-CBMS Regional Conf. Math., 40. , Amer. Math. Soc., Providence, RI
  • Mawhin, J., Landesman-Lazer conditions for boundary value problems: A nonlinear version of resonance (2000) Bol. Soc. Esp. Mat. Apl., 16, pp. 45-65
  • Mawhin, J., Ureña, A.J., A Hartman-Nagumo inequality for the vector ordinary p-Laplacian and applications to nonlinear boundary value problems (2002) J. Inequal. Appl., 7 (5), pp. 701-725
  • Nirenberg, L., Generalized degree and nonlinear problems (1971) Contributions to Nonlinear Functional Analysis, pp. 1-9. , Zarantonello E.H. (Ed), Academic Press, New York
  • Nagumo, M., Über die Differentialgleichung y″ = f (t, y, y′) (1937) Proc. Phys. Math. Soc. Japan, 19, pp. 861-866
  • Ortega, R., Sánchez, L., Periodic solutions of forced oscillators with several degrees of freedom (2002) Bull. London Math. Soc., 34, pp. 308-318

Citas:

---------- APA ----------
Amster, P. & De Nápoli, P. (2007) . Landesman-Lazer type conditions for a system of p-Laplacian like operators. Journal of Mathematical Analysis and Applications, 326(2), 1236-1243.
http://dx.doi.org/10.1016/j.jmaa.2006.04.001
---------- CHICAGO ----------
Amster, P., De Nápoli, P. "Landesman-Lazer type conditions for a system of p-Laplacian like operators" . Journal of Mathematical Analysis and Applications 326, no. 2 (2007) : 1236-1243.
http://dx.doi.org/10.1016/j.jmaa.2006.04.001
---------- MLA ----------
Amster, P., De Nápoli, P. "Landesman-Lazer type conditions for a system of p-Laplacian like operators" . Journal of Mathematical Analysis and Applications, vol. 326, no. 2, 2007, pp. 1236-1243.
http://dx.doi.org/10.1016/j.jmaa.2006.04.001
---------- VANCOUVER ----------
Amster, P., De Nápoli, P. Landesman-Lazer type conditions for a system of p-Laplacian like operators. J. Math. Anal. Appl. 2007;326(2):1236-1243.
http://dx.doi.org/10.1016/j.jmaa.2006.04.001