Study of the solution semigroup for integral equations and related topics

研究了积分方程解的一些定性性质。实际上，对于线性积分方程，我们分析了关联解半群生成子的一些谱性质，并得到了生成子的本质谱半径的估计。在此基础上，建立了非齐次线性方程解的相空间表示公式。应用这些结果，我们得到了关于有界解、周期解等存在性的Massera型结果。对于非线性积分方程，我们建立了线性化原理，该原理有效地适用于非线性方程的稳定性问题。

We studied some qualitative properties of solutions in integral equations. Indeed, for linear integral equations we analyzed some spectral properties for the generator of the associated solution semigroup, and obtained an estimate on the essential spectral radius of the generator. Furthermore, we established a representation formula in the phase space for solutions of nonhomogeneous linear equations. Applying these results, we obtained Massera type results on the existence of bounded solutions, periodic solutions and so on. Also, for nonlinear integral equations we established the principle of linearization which is effectively applicable to stability problems in nonlinear equations.