一类Banach空间中的完全二阶线性微分方程的适定性和指数增长性

ON THE WELL-POSEDNESS AND THE EXPONENTIAL GROWTH OF SOLUTIONS OF SOME COMPLETE SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS IN BANACH SPACE

讨论了A为有界线性算子情形下的Banach空间中的完全二阶线性微分方程的Cauchy问题的适定性和解的指数增长性,得到了一些充分必要条件.

We discuss the well-posedness of Cauchy problems and the exponenlial growth of solutions for the complete second order linear differential equation u+Bu+Au=0 under the assumption that A is bounded, and obtain some sufficient and necessary conditions.