中文摘要：

在Hilbert空间框架下研究一类半线性发展方程非局部问题解的正则性,在非线性项满足次线性增长条件的情形下,运用解析半群理论及全连续算子的Leray-Schauder不动点定理,通过累次正则的方法,获得该问题强解的存在性。给出抛物型偏微分方程非局部问题的实例,说明所得抽象结果的可行性。

英文摘要：

The regularity of the solutions for nonlocal problem of a class of semilinear evolution equations is studied in a frame of Hilbert space.By applying the theory of analytic semigroups,Leray-Schauder fixed point theorem with respect to completely continuous operator and the method of iterated regular,the existence of strong solutions is obtained under sublinear growth condition of the nonlinear term.At last,an example of concrete parabolic partial differential equations with nonlocal conditions is also given to illustrate the feasibility of the obtained abstract results.