BIFURCATION AND STABILITY OF SPATIALLY PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS WITH INTEGRAL OPERATORS

Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (11): 1045-1056.

BIFURCATION AND STABILITY OF SPATIALLY PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS WITH INTEGRAL OPERATORS

陆启韶

Beijing Institute of Aeronautics and Astronautics, Beijing

收稿日期:1986-07-19 出版日期:1987-11-18 发布日期:1987-11-18
通讯作者: Guo Zhong-heng
基金资助:
the Chinese National Foundation of Natural Science

BIFURCATION AND STABILITY OF SPATIALLY PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS WITH INTEGRAL OPERATORS

Lu Qi-shao

Beijing Institute of Aeronautics and Astronautics, Beijing

Received:1986-07-19 Online:1987-11-18 Published:1987-11-18
Supported by:
the Chinese National Foundation of Natural Science

摘要/Abstract

摘要： A more general kind of nonlinear evolution equations with integral operators is discussed in order to study the spatially periodic static bifurcating solutions and their stability. At first, the necessary condition and the sufficient condition for the existence of bifurcation are studied respectively. The stability of the equilibrium solutions is analyzed by the method of semigroups of linear operators. We also obtain the principle of exchange of stability in this case. As an example of application, a concrete result for a special case with integral operators of exponential type is presented.

关键词: ENSO, limit cycle, self-exited oscillation

Abstract: A more general kind of nonlinear evolution equations with integral operators is discussed in order to study the spatially periodic static bifurcating solutions and their stability. At first, the necessary condition and the sufficient condition for the existence of bifurcation are studied respectively. The stability of the equilibrium solutions is analyzed by the method of semigroups of linear operators. We also obtain the principle of exchange of stability in this case. As an example of application, a concrete result for a special case with integral operators of exponential type is presented.

Key words: ENSO, limit cycle, self-exited oscillation

陆启韶. BIFURCATION AND STABILITY OF SPATIALLY PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS WITH INTEGRAL OPERATORS[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(11): 1045-1056.

Lu Qi-shao . BIFURCATION AND STABILITY OF SPATIALLY PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS WITH INTEGRAL OPERATORS[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(11): 1045-1056.

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BIFURCATION AND STABILITY OF SPATIALLY PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS WITH INTEGRAL OPERATORS

BIFURCATION AND STABILITY OF SPATIALLY PERIODIC SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS WITH INTEGRAL OPERATORS

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