DOI:
https://doi.org/10.14483/udistrital.jour.RC.2016.27.a9Published:
12/27/2016Issue:
Vol. 27 No. 3 (2016): September-December 2016Section:
Science and EngineeringBifurcación de Soluciones desde Infinito en un Valor Propio de Multiplicidad Infinita a un Problema Hiperbólico Semilineal Doble-Periódico
Bifurcation of Solutions from Infinity at an Infinity Multiplicity Eigenvalue for a Semilinear Double-Periodic Hyperbolic Problem
Keywords:
ecuación de onda semilineal, bifurcación desde infinito (es).Downloads
Abstract (es)
Estudiamos la existencia de soluciones débiles a la ecuación de onda sujeta a las condiciones doble-periódicas . Cuando las soluciones tienden a infinito. No estamos suponiendo monotonía sobre la nolinealidad . Empleamos métodos de Teoría de Grado de Leray-Schauder y Principio de Contracciones.
Abstract (en)
We consider the existence of weak solutions to the wave equationssubject to the double-periodic conditions . Whenthe solutions goes to infinity. We are no assuming monotonicity on the nonlinearity . We use Leray-Schauder Degree Theory and Contraction Principle.
References
Brézis , H., Coron , J. M. & Nirenberg , L. (1980). Free Vibrations for a Nonlinear Wave Equation and a Theorem of P. Rabinowitz. En: Communications on Pure and Applied Mathematics. XXXIII p. 667#689
Brooks, R. M. & Schmitt. K. (2009). The Contraction Mapping Principle and Some Applications. Electronic journal of differential equations: Monograph.
Caicedo, J. F. & Castro, A. (1997). A Semilinear Wave Equation with Derivative of Nonlinearity Containing Multiple Eigenvalues of Infinite Multiplicity. Contemporary Mathematics: 208.
Caicedo , J. F., Castro , A., Duque , R. & Sanjuán A. (2014). Existence of for a semilinear wave equation with non-monotone nonlinearity. En: Discrete and Continuous Dynamical Systems 7 , Nr. 69, p. 1193#1202.
Caicedo, J. F., Castro, A. & Sanjuán, A. (2016). Bifurcación at Infinity for a Semilinear Wave Equation. (prepint)
Castro, A. & Preskill, B. (2010). Existence of Solutions for a Wave Equation with Nonmonotone Nonlinearity. En: Discrete and Continuous Dynamical Systems 28 Nr. 2, p. 549#658.
Hofer, H. (1982). On the range of a wave operator with nonmonotone nonlinearity. En: Nachr. Math. , Nr. 106, p. 327#340.
Iorio, R. & Magalhaes, V. (2001). Fourier Analysis and Partial Differential Equations. Cambridge Studies in Advanced Mathematicas.
Kung-Ching, C. (2005) Methods in Nonlinear Analyisis. Springer-Verlag, Berlin.
Lovicarová H. (1968). Periodic Solutions of a Weakly Nonlinear Wave Equation in one Dimention. En: Czecnosiovak Mathematical Journal. 19 (1968), Nr. 94, p. 324#343
Rabinowitz, P. (1967). Periodic Solutions of Nonlinear Hyperbolic Partial Diffrential Equations. En: Communications on Pure and Applied Mathematics XX , p. 145#205.
Rabinowitz, P. (1978). Free Vibrations for a Semilinear Wave Equation. En: Communications on Pure and Applied Mathematics XXXI, p. 31#68
Sanjuán (2015). Membranas Vibrantes. Tesis Doctoral Universidad Nacional de Colombia.
Rabinowitz, P. (1971). Some global results for nonlinear eigenvalue problems. En: Journal of Functional Analysis 7 , Nr. 3, p. 487#513.
Willem, M. (1981) Density of the Range of Potential Operators. En: Proceedings of the American Mathematical Society 83 , Nr. 2, p. 341#344
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