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Abstract:

A nonlinear elliptic second order system with a nonlinear boundary condition is studied. We prove an existence result under a Hartman type condition. Moreover, assuming appropriate conditions of Nirenberg type, we prove the existence of solutions applying topological degree theory. Copyright © 2009, Inderscience Publishers.

Registro:

Documento: Artículo
Título:Topological methods for a nonlinear elliptic system with nonlinear boundary conditions
Autor:Amster, P.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, 1428 Buenos Aires, Argentina
Consejo Nacional de Investigaciones Cientificas y Técnicas (CONICET), Buenos Aires, Argentina
Palabras clave:Leray-Schauder degree; Nonlinear boundary conditions; Nonlinear elliptic systems; Existence of Solutions; Existence results; Leray-Schauder degree; Nonlinear boundary conditions; Nonlinear elliptic systems; Second-order systemss; Topological degree theory; Topological methods; Geometry; Boundary conditions
Año:2009
Volumen:2
Número:1-2
Página de inicio:56
Página de fin:65
DOI: http://dx.doi.org/10.1504/IJDSDE.2009.028035
Título revista:International Journal of Dynamical Systems and Differential Equations
Título revista abreviado:Int. J. Dyn. Syst. Differ. Equ.
ISSN:17523583
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17523583_v2_n1-2_p56_Amster

Referencias:

  • Amster, P., De Nápoli, P., Landesman-Lazer type conditions for a system of p-Laplacian like operators (2007) Journal of Mathematical Analysis and Applications, 326, pp. 1236-1243
  • Fernández Bonder, J., Rossi, J., Existence results for the p-Laplacian with nonlinear boundary conditions (2001) Journal of Mathematical Analysis and Applications, 263, pp. 195-223
  • Gaines, R., Mawhin, J., Coincidence Degree and Nonlinear Differential Equations (1997) Lecture Notes in Math, 568. , Springer, New York
  • Grossinho, M., Ma, T.F., Symmetric equilibria for a beam with a nonlinear elastic foundation (1994) Portugaliae Mathematica, 51, pp. 375-393
  • Hartman, P., On boundary valuie problems ofr systems of ordinary nonlinear second order differential equtions (1960) Trnas. Amer. Math. Soc, 96, pp. 493-509
  • Knobloch, W., On the existence of periodic solutions for second order vector dilerential equations (1971) J. Differential Equations, 9, pp. 67-85
  • Martínez, S., Rossi, J., Weak solutions for the p laplacian with a nonlinear boundary condition at resonance (2003) Electronic Journal of Differential Equations, 2003 (27), pp. 1-14
  • Mawhin, J., Topological degree methods in nonlinear boundary value problems (1979) NSF-CBMS Regional Conference in Mathematics, (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 Matemática Aplicada, 16, pp. 45-65
  • Mawhin, J., Ureña, A., A Hartman-Nagumo inequality for the vector ordinary p-Laplacian and applications to nonlinear boundary value problems (2002) Journal of Inequalities and Applications, 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, pp
  • 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

Citas:

---------- APA ----------
(2009) . Topological methods for a nonlinear elliptic system with nonlinear boundary conditions. International Journal of Dynamical Systems and Differential Equations, 2(1-2), 56-65.
http://dx.doi.org/10.1504/IJDSDE.2009.028035
---------- CHICAGO ----------
Amster, P. "Topological methods for a nonlinear elliptic system with nonlinear boundary conditions" . International Journal of Dynamical Systems and Differential Equations 2, no. 1-2 (2009) : 56-65.
http://dx.doi.org/10.1504/IJDSDE.2009.028035
---------- MLA ----------
Amster, P. "Topological methods for a nonlinear elliptic system with nonlinear boundary conditions" . International Journal of Dynamical Systems and Differential Equations, vol. 2, no. 1-2, 2009, pp. 56-65.
http://dx.doi.org/10.1504/IJDSDE.2009.028035
---------- VANCOUVER ----------
Amster, P. Topological methods for a nonlinear elliptic system with nonlinear boundary conditions. Int. J. Dyn. Syst. Differ. Equ. 2009;2(1-2):56-65.
http://dx.doi.org/10.1504/IJDSDE.2009.028035