We study the existence of mild solutions for a nonlocal semilinear evolution equation on unbounded interval by means of an approximation solvability method without assuming compactness on the evolution system and on the nonlinearity. The method is based on the reduction to a finite dimensional problem by means of the projections solved by a fixed point approach that includes a compactness criterion on $\mathcal{BC}([0,+\infty ),E)$. Continuation principle and weak topology are used as well.

中文翻译：

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自反Banach空间中非局部半线性发展方程在无限区间上的温和解。

我们通过近似可解性方法研究了无界区间上非局部半线性发展方程的温和解的存在性，而没有假设系统和非线性的紧凑性。该方法基于通过固定点方法求解的投影简化为有限维问题，其中固定点方法包括$\mathcal{公元前}（[0，+\infty ），Ë）$。还使用了延续原理和弱拓扑。