Research and Innovation Articles
Published 2009-09-03
Keywords
- Teorema generalizado de Rouché,
- operadores Fredholm,
- ecuación tipo Boussinesq
How to Cite
Diaz, G. A. (2009). Una generalización para operadores del teorema de Rouché. Revista Integración, Temas De matemáticas, 26(2), 97–115. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/180
Abstract
Rouché's theorem is used to study the zeros of a function in a contour, when the zeros of another related function are known. This paper generalizes that theorem for the case of operators. Also, it is shown an application associated with an operator related to the linearization of a Boussinesq type equation.
Downloads
Download data is not yet available.
References
[1] Lars V. Ahlfors, Análisis de variable compleja, McGraw-Hill Book Company, Madrid, 1966.
[2] G. Arenas, Valores propios de la linealización de una ecuación tipo Boussinesq, vía el teorema generalizado de Rouché, Tesis de Maestría, Universidad del Valle, Cali, 2003.
[3] I.C. Gohberg & E.I. Sigal, “An Operator Generalization of the Logarithmic Residue Theorem and the Theorem of Rouché”, Mat. Issled. Vol. 13, No. 4, 603-625, (1971).
[4] R. Pego & M. Weinstein, “Asymptotic Stabilities of Solitary Waves”, Phil. Trans. Roy. Soc. London A340: 305-349, (1994).
[5] R. Pego & M. Weinstein, “Convective Linear Stability of Solitary Waves for Boussinesq Equation”, AMS, No. 99, 311-375, (1997).
[6] J.R. Quintero & G. Arenas, “The Eigenvalue Problem for Solitary Waves of a Boussinesq Equation, via a Generalization of the Rouché Theorem”, Applicable Analysis, Vol. 83, No. 12, 1211–1228, (2004).
[2] G. Arenas, Valores propios de la linealización de una ecuación tipo Boussinesq, vía el teorema generalizado de Rouché, Tesis de Maestría, Universidad del Valle, Cali, 2003.
[3] I.C. Gohberg & E.I. Sigal, “An Operator Generalization of the Logarithmic Residue Theorem and the Theorem of Rouché”, Mat. Issled. Vol. 13, No. 4, 603-625, (1971).
[4] R. Pego & M. Weinstein, “Asymptotic Stabilities of Solitary Waves”, Phil. Trans. Roy. Soc. London A340: 305-349, (1994).
[5] R. Pego & M. Weinstein, “Convective Linear Stability of Solitary Waves for Boussinesq Equation”, AMS, No. 99, 311-375, (1997).
[6] J.R. Quintero & G. Arenas, “The Eigenvalue Problem for Solitary Waves of a Boussinesq Equation, via a Generalization of the Rouché Theorem”, Applicable Analysis, Vol. 83, No. 12, 1211–1228, (2004).