Sentence examples for solutions for evolution from inspiring English sources

Since then, much attention has been paid to studying the complicated asymptotic behavior of solutions for evolution equations [9 11].

The works mentioned above mainly establish the existence of mild solutions for evolution equations or inclusions with nonlocal conditions.

In this work, we study the existence of bounded and almost automorphic solutions for evolution equations in Banach spaces.

However, most of the existing articles only studied the existence and uniqueness of mild solutions for evolution equations with nonlocal conditions, there are very few papers considered the regularity results for nonlocal evolution equations.

The existence of almost automorphic and pseudo-almost automorphic solutions for evolution equations with linear part dominated by a Hille-Yosida type operator constitutes an untreated topic and this fact is the main motivation of this paper.

The term (I_{i}(x(t_{i}))) means that the impulses are also related to the value of (x(t_{i})=x(t^_{i})). From the results obtained in the papers [21 24], we know that the definition of mild solutions for fractional evolution equations is more involved than integer order evolution equations.

However, we observed that all of the existing articles are only devoted to the study of the existence, uniqueness, and controllability of mild solutions for fractional evolution equations; up to now the continuous dependence of mild solutions on parameters for fractional evolution equations has not been considered in the literature.

In this article, we established abundant traveling wave solutions for nonlinear evolution equations.

The study of anti-periodic solutions for nonlinear evolution equations was initiated by Okochi [1].

He and Abdou [16] have used EFM to give new periodic solutions for nonlinear evolution equations.

And he firstly found the phenomenon of vacuum isolating of solutions for nonlinear evolution equations.