Nonlocal Cauchy problems for semilinear evolution equations (Q1612563)

Here, the authors study the existence and uniqueness of mild and classical solutions to nonlocal Cauchy problems for semilinear evolution equations. They first establish an existence and uniqueness result for the continuous solution to a general convolution integral equation in a Banach space and then apply this to yield existence and uniqueness results for mild and classical solutions to nonlocal Cauchy problems for semilinear evolution equations. An example which illustrates the theoretical results is also presented.