Global mild solutions for the nonautonomous 2D Navier-Stokes equations with impulse effects

一类具不同分数阶扩散的偏微分方程组温和解的爆破

Blow up of mild solutions of a system of partial differential equations with distinct fractional diffusions

本文给出了一类具有不同分数阶扩散的非自治弱耦合系统的初值问题正温和解爆破的一个充分条件。证明是基于一个特殊的常微分方程系统的爆破研究。

非自治Schrödinger-Poisson方程的归一化解

Normalized solutions for nonautonomous Schrödinger-Poisson equations

本文研究非自治Schrödinger-Poisson方程归一化解的存在性，利用Pohozaev流形恢复极小化序列紧性，并针对p的三个不同区间采用不同分析技巧克服能量泛函中三项伸缩不一致的困难。

Existence of Fractional Nonlocal Neutral Stochastic Differential Equation of Order 1 < q < 2 with Non-instantaneous Impulses and State-Dependent Delay

This article addresses a new class of fractional nonlocal neutral stochastic differential system of order 1<q<2 including non-instantaneous impulses(NIIs) and state-dependent delay(SDD) with the Poisson jumps and the Wiener process in Hilbert spaces. We examine the existence of a mild solution without assuming the compactness of the resolvent operators. The Monch fixed point theorem is used along with the Hausdorff measure of noncompactness. An example is constructed to verify the theoretical developments.

Existence and Asymptotic Stability of Periodic Solutions for Impulsive Delay Evolution Equations

In this paper, we are devoted to consider the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroups theory and fixed point theorem, we establish some new existence theorems of periodic mild solutions for the equations. In addition, with the aid of an integral inequality with impulsive and delay, we present essential conditions on the nonlinear and impulse functions to guarantee that the equations have an asymptotically stable $ω$-periodic mild solution.