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Abstract:

We study a nonlinear problem of pendulum-type for a p-Laplacian with nonlinear periodic-type boundary conditions. Using an extension of Mawhin's continuation theorem for nonlinear operators, we prove the existence of a solution under a Landesman-Lazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum equation. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Registro:

Documento: Artículo
Título:A nonlinear second order problem with a nonlocal boundary condition
Autor:Amster, P.; De Nápoli, P.
Filiación:Universidad de Buenos Aires, FCEyN, Pabellón I, (1428) Buenos Aires, Argentina
Año:2006
Volumen:2006
Página de inicio:1
Página de fin:11
DOI: http://dx.doi.org/10.1155/AAA/2006/38532
Título revista:Abstract and Applied Analysis
Título revista abreviado:Abstr. Appl. Anal.
ISSN:10853375
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_10853375_v2006_n_p1_Amster.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10853375_v2006_n_p1_Amster

Referencias:

  • Amster, P., De Nápoli, P., Mariani, M.C., Existence of solutions to N-dimensional pendulum-like equations (2004) Electronic Journal of Differential Equations, 2004 (125), pp. 1-8
  • Berestycki, H., Brézis, H., On a free boundary problem arising in plasma physics (1980) Nonlinear Analysis, 4 (3), pp. 415-436
  • Castro, A., Periodic solutions of the forced pendulum equation (1979) Differential Equations Proc. Eighth Fall Conf., pp. 149-160. , Oklahoma State Univ., Stillwater, Okla., Academic Press, New York
  • Dibenedetto, E., C1+α local regularity of weak solutions of degenerate elliptic equations (1983) Nonlinear Analysis, 7 (8), pp. 827-850
  • Dinca, G., Jebelean, P., Mawhin, J., Variational and topological methods for Dirichlet problems with p-Laplacian (2001) Portugaliae Mathematica. Nova Série, 58 (3), pp. 339-378
  • Drábek, P., Girg, P., Takáč, P., Bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity (2004) Journal of Differential Equations, 204 (2), pp. 265-291
  • Fournier, G., Mawhin, J., On periodic solutions of forced pendulum-like equations (1985) Journal of Differential Equations, 60 (3), pp. 381-395
  • Ge, W., Ren, J., An extension of Mawhin's continuation theorem and its application to boundary value problems with a p-Laplacian (2004) Nonlinear Analysis, 58 (3-4), pp. 477-488
  • Landesman, E.M., Lazer, A.C., Nonlinear perturbations of linear elliptic boundary value problems at resonance (1970) J. Math. Mechanics, 19, pp. 609-623
  • Le, V.K., Schmitt, K., Sub-supersolution theorems for quasilinear elliptic problems: A variational approach (2004) Electronic Journal of Differential Equations, 2004 (118), pp. 1-7
  • Manásevich, R., Mawhin, J., Periodic solutions for nonlinear systems with p-Laplacian-like operators (1998) Journal of Differential Equations, 145 (2), pp. 367-393
  • Mawhin, J., Topological degree methods in nonlinear boundary value problems (1979) CBMS Regional Conference Series in Mathematics, 40. , American Mathematical Society, Rhode Island
  • Ni, X., Ge, W., Multi-point boundary-value problems for the p-Laplacian at resonance (2003) Electronic Journal of Differential Equations, 2003 (112), pp. 1-7
  • Tolksdorf, P., Regularity for a more general class of quasilinear elliptic equations (1984) Journal of Differential Equations, 51 (1), pp. 126-150

Citas:

---------- APA ----------
Amster, P. & De Nápoli, P. (2006) . A nonlinear second order problem with a nonlocal boundary condition. Abstract and Applied Analysis, 2006, 1-11.
http://dx.doi.org/10.1155/AAA/2006/38532
---------- CHICAGO ----------
Amster, P., De Nápoli, P. "A nonlinear second order problem with a nonlocal boundary condition" . Abstract and Applied Analysis 2006 (2006) : 1-11.
http://dx.doi.org/10.1155/AAA/2006/38532
---------- MLA ----------
Amster, P., De Nápoli, P. "A nonlinear second order problem with a nonlocal boundary condition" . Abstract and Applied Analysis, vol. 2006, 2006, pp. 1-11.
http://dx.doi.org/10.1155/AAA/2006/38532
---------- VANCOUVER ----------
Amster, P., De Nápoli, P. A nonlinear second order problem with a nonlocal boundary condition. Abstr. Appl. Anal. 2006;2006:1-11.
http://dx.doi.org/10.1155/AAA/2006/38532