Second-order nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls on Banach spaces

作者：Peng Y^*; Xiang X; Wei W

来源：Computers & Mathematics with Applications, 2009, 57(1): 42-53.

DOI：10.1016/j.camwa.2008.09.029

• Unbounded time-varying operator matrix
• Integral operator of mixed type
• Compactness
• Existence
• Optimal control

In this paper, a class of second-order nonlinear impulsive integro-differential equations of mixed type whose principle is time-varying generating operators with unbounded perturbation on Banach spaces is considered. Discussing the perturbation of time-varying operator matrix and constructing corresponding the evolution system generated by operator matrix. we introduce the reasonable mild solution of second-order nonlinear impulsive integro-differential equations of mixed type and prove the existence of mild solutions. The existence of optimal controls for a Lagrange problem of systems governed by the second-order nonlinear impulsive integro-equations of mixed type is also presented. An example is given for demonstration.

• 出版日期2009-1
• 单位贵州大学