有积分算子的非线性发展方程的空间周期分叉解及其稳定性*

本文研究比较一般的有积分算子的非线性发展方程的空间周期分叉解及稳定性问题。首先分别研究分叉解存在的必要条件和充分条件,然后用算子半群方法分析平衡解的稳定性,并讨论了稳定性交换原则。最后研究一个应用例子,对有指数型积分算子的情形得到具体结果。

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

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.