Termination of a pinned spiral wave by the wave train with a free defect

Nonlinear Dynamics - Spiral waves in the cardiac tissue may cause life-threatening arrhythmia. Such waves can be anchored to a local heterogeneity and form stable pinned waves, which are difficult...     

分析化学实验教学改革与实践

在教学实践中对分析化学实验教学进行了改革与探索。从提高学生基本素质、基本技能、综合实验能力出发,探索培养具有创新性的高素质、高质量社会需要人才的教学方式与方法。     

Ground state solutions for asymptotically periodic fractional Schrödinger–Poisson problems with asymptotically cubic or super‐cubic nonlinearities

In this paper, we consider the following fractional Schrödinger–Poisson problem: where s,t∈(0,1],4s+2t>3,V(x),K(x), and f(x,u) are periodic or asymptotically periodic in x. We use the non‐Nehari manifold approach to establish the existence of the Nehari‐type ground state solutions in two cases: the periodic one and the asymptotically periodic case, by introducing weaker conditions uniformly in with and with constant θ₀∈(0,1), instead of uniformly in and the usual Nehari‐type monotonic condition on f(x,τ)/|τ|³. Our results unify both asymptotically cubic or super‐cubic nonlinearities, which are new even for s=t=1. Copyright © 2017 John Wiley & Sons, Ltd.     

Ground state solutions of Nehari–Pohozaev type for Kirchhoff-type problems with general potentials

This paper is dedicated to studying the following Kirchhoff-type problem

$$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\left( a+b\int _{\mathbb {R}^3}|\nabla u|^2\mathrm {d}x\right) \triangle u+V(x)u=f(u), &{} x\in \mathbb {R}^3; \\ u\in H^1(\mathbb {R}^3), \end{array} \right. \end{aligned}$$

(0.1)

where \(a>0,\,b\ge 0\) are two constants, V(x) is differentiable and \(f\in \mathcal {C}(\mathbb {R}, \mathbb {R})\). By introducing some new tricks, we prove that the above problem admits a ground state solution of Nehari–Pohozaev type and a least energy solution under some mild assumptions on V and f. Our results generalize and improve the ones in Guo (J Differ Equ 259:2884–2902, 2015) and Li and Ye (J Differ Equ 257:566–600, 2014) and some other related literature.

     

Ground state solutions to logarithmic Choquard equations in R3

In this paper, we prove the existence of nontrival solutions of mountain-pass type, least energy solutions and ground state solutions for logarithmic Choquard equation. Some new variational methods and techniques are used in the present paper and we extend and improve the present ones in the literature.     

On the Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with General Potentials and Super-quadratic Nonlinearity

In this article, we are concerned with the following fractional Schrödinger–Poisson system:

$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}u+V(x)u+\phi u=f(u)&{} \quad \hbox {in}~\mathbb {R}^{3},\\ (-\Delta )^{t}\phi =u^2&{} \quad \hbox {in}~\mathbb {R}^{3},\\ \end{array} \right. \end{aligned}$$

where \(0<s\le t<1\), \(2s+2t>3\), and \(f\in C(\mathbb {R},\mathbb {R})\). Under more relaxed assumptions on potential V(x) and f(x), we obtain the existence of ground state solutions for the above problem by adopting some new tricks. Our results here extend the existing study.