Mild solutions of semilinear evolution equation on an unbounded interval and their applications

The aim of this paper is to give an existence theorem for a semilinear equation of evolution on an unbounded interval in the case when the generator of a semigroup depends on time parameter. The considerations of this paper are based on the concept of a measure of noncompactness in Fréchet space and the classical Tichonov fixed point principle. Moreover, an application of the main theorem to the second-order parabolic PDE is given.