Bifurcation and Stability of Spatially Periodic Solutions of Nonlinear Evolution Equations with Integral Operators

Lu Qi-shao

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Article Navigation > Applied Mathematics and Mechanics > 1987 > 8(11): 985-995

Lu Qi-shao. Bifurcation and Stability of Spatially Periodic Solutions of Nonlinear Evolution Equations with Integral Operators[J]. Applied Mathematics and Mechanics, 1987, 8(11): 985-995.

Citation:

Lu Qi-shao. Bifurcation and Stability of Spatially Periodic Solutions of Nonlinear Evolution Equations with Integral Operators[J]. Applied Mathematics and Mechanics, 1987, 8(11): 985-995.

Citation:

Lu Qi-shao. Bifurcation and Stability of Spatially Periodic Solutions of Nonlinear Evolution Equations with Integral Operators[J]. Applied Mathematics and Mechanics, 1987, 8(11): 985-995.

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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 Date: 1986-07-19
Publish Date: 1987-11-15

Abstract

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.

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References(9)

References

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