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Abstract:

Existence of solutions for a nonlinear fourth order ordinary differential equation arising in beam theory is considered. We obtain solutions by a degree argument under a non-asymptotic condition on the nonlinear terms of the problem. Moreover, assuming a potential Landesman-Lazer condition, we prove the existence of at least one solution by variational methods. © 2012 Korean Society for Computational and Applied Mathematics.

Registro:

Documento: Artículo
Título:Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation
Autor:Amster, P.
Filiación:Departamento de Matemática, FCEyN, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
Palabras clave:Degree theory; Landesman-Lazer conditions; Nonlinear beam equation; Symmetric solutions; Variational methods; Degree theory; Landesman-Lazer condition; Nonlinear beam equation; Symmetric solution; Variational methods; Ordinary differential equations; Continuum mechanics
Año:2012
Volumen:40
Número:1-2
Página de inicio:63
Página de fin:72
DOI: http://dx.doi.org/10.1007/s12190-012-0552-1
Título revista:Journal of Applied Mathematics and Computing
Título revista abreviado:J. Appl. Math. Comp.
ISSN:15985865
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15985865_v40_n1-2_p63_Amster

Referencias:

  • Amster, P., Cárdenas Alzate, P.P., Existence of solutions for some nonlinear beam equations (2006) Port. Math., 63 (1), pp. 113-125. , 2211965 1107.34010
  • Grossinho, M., Ma, T.F., Symmetric equilibria for a beam with a nonlinear elastic foundation (1994) Port. Math., 51, pp. 375-393. , 1295208 0815.34014
  • Landesman, E., Lazer, A., Nonlinear perturbations of linear elliptic boundary value problems at resonance (1970) J. Math. Mech., 19, pp. 609-623. , 267269 0193.39203
  • Mawhin, J., Topological degree methods in nonlinear boundary value problems (1979) NSF-CBMS Regional Conference in Mathematics, , 40 Amer. Math. Soc. Providence
  • Mawhin, J., Landesman-Lazer conditions for boundary value problems: A nonlinear version of resonance (2000) Bol. Soc. Española Mat. Apl., 16, pp. 45-65
  • Rabinowitz, P., Some minimax theorems and applications to partial differential equations (1978) Nonlinear Analysis: A Collection of Papers in Honor of Erich Röthe, pp. 161-177. , Academic Press New York

Citas:

---------- APA ----------
(2012) . Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation. Journal of Applied Mathematics and Computing, 40(1-2), 63-72.
http://dx.doi.org/10.1007/s12190-012-0552-1
---------- CHICAGO ----------
Amster, P. "Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation" . Journal of Applied Mathematics and Computing 40, no. 1-2 (2012) : 63-72.
http://dx.doi.org/10.1007/s12190-012-0552-1
---------- MLA ----------
Amster, P. "Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation" . Journal of Applied Mathematics and Computing, vol. 40, no. 1-2, 2012, pp. 63-72.
http://dx.doi.org/10.1007/s12190-012-0552-1
---------- VANCOUVER ----------
Amster, P. Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation. J. Appl. Math. Comp. 2012;40(1-2):63-72.
http://dx.doi.org/10.1007/s12190-012-0552-1