Nonlocal Cauchy problems for semilinear evolution equations. (English) Zbl 1009.34052

Liang, Jin; van Casteren, J.; Xiao, Ti-Jun

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 50, No. 2, 173-189 (2002).

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.

Reviewer: S.K.Ntouyas (Ioannina)

MSC:

34G20

Nonlinear differential equations in abstract spaces

Keywords:

nonlocal Cauchy problem; semilinear evolution equation; convolution integralequation; regularized semigroups; fractional powers

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