T-controllability for a class of second order neutral evolution equations under integral contractor conditions(积分收缩条件下一类二阶中立型发展方程的T-可控性)

The existence, uniqueness and T-controllability of mild solution for a class of second order neutral evolution equations are studied in Hilbert space. By using the cosine family theory, regular integral contractor conditions (weaker condition than Lipschitz continuous) and iterative technique, we get the existence and uniqueness of the mild solution of the studied problem, and the sufficient conditions for the T-controllability of the problem are obtained by combining the assumptions of monotonicity and coercivity of the operator. Finally, an example is delivered to illustrate the gained theoretical results.(研究了在Hilbert空间中的一类二阶中立型发展方程适度解的存在唯一性和T-可控性。利用余弦族理论、正则积分收缩条件（较Lipschitz连续弱的条件）和迭代技术，证明了一类二阶中立型发展方程适度解的存在唯一性，并结合算子的单调性与强制性假设，获得了其T-可控性的充分条件。最后，通过实例验证了结果的正确性。)