## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

CPAA

In this paper, we make an exhaustive
study of the third order linear operators $u''' +Mu$, $u'''+Mu'$ and
$u'''+Mu''$ coupled with $(k, 3-k)$-conjugate boundary conditions,
where $k=1,2$. We obtain the optimal intervals on which the Green's functions are of one sign. The main tool is the disconjugacy
theory. As an application of our results, we develop a monotone
iteration method to obtain positive solutions of the nonlinear
problem $u'''+Mu''+f(t,u)=0$, $u(0)=u'(0)=u(1)=0$.

DCDS

In this paper, we establish a unilateral global bifurcation result from interval for a class of $p$-Laplacian problems.
By applying above result, we study the spectrum of a class of half-quasilinear problems.
Moreover, we also investigate the existence of nodal solutions for a class of half-quasilinear eigenvalue problems.

CPAA

In this paper, we establish a unilateral global bifurcation result for a class of quasilinear periodic boundary problems with a sign-changing weight.
By the Ljusternik-Schnirelmann theory, we first study the spectrum of the periodic $p$-Laplacian with the sign-changing weight.
In particular, we show that there exist two simple, isolated, principal eigenvalues $\lambda_0^+$ and $\lambda_0^-$.
Furthermore, under some natural hypotheses on perturbation function,
we show that $(\lambda_0^\nu,0)$ is a bifurcation
point of the above problems and there are two distinct unbounded sub-continua
$C_\nu^{+}$ and $C_\nu^{-}$,
consisting of the continuum $C_\nu$ emanating from $(\lambda_0^\nu, 0)$,
where $\nu\in\{+,-\}$. As an application of the above result, we study the existence of one-sign solutions
for a class of quasilinear periodic boundary problems with the sign-changing weight.
Moreover, the uniqueness of one-sign solutions and the dependence of solutions on the parameter $\lambda$ are
also studied.

DCDS-B

This paper is concerned with the traveling waves of a nonlocal dispersal Lotka-Volterra strong competition model with bistable nonlinearity. We first establish the asymptotic behavior of traveling waves at infinity. Then by applying the stronger comparison principle and the sliding method, we prove that the traveling waves with nonzero speed are strictly monotone. Moreover, the uniqueness of wave speeds is also obtained.

keywords:
Nonlocal dispersal
,
strong competition system
,
traveling waves
,
monotonicity
,
uniqueness
,
wave speed

DCDS-B

In recent years, online social networks such as Twitter, have become a major source of information exchange and research on information diffusion in social networks has been accelerated. Partial differential equations are proposed to characterize temporal and spatial patterns of information diffusion over online social networks. The new modeling approach presents a new analytic framework towards quantifying information diffusion through the interplay of structural and topical influences. In this paper we develop a non-autonomous diffusive logistic model with indefinite weight and the Robin boundary condition to describe information diffusion in online social networks. It is validated with a real dataset from an online social network, Digg.com. The simulation shows that the logistic model with the Robin boundary condition is able to more accurately predict the density of influenced users. We study the bifurcation, stability of the diffusive logistic model with heterogeneity in distance. The bifurcation and stability results of the model information describe either information spreading or vanishing in online social networks.

DCDS-B

Let $B_1$ be the unit ball in $\mathbb{R}^N$ with $N \geq 2$. Let $f\in C^1([0, \infty), \mathbb{R})$, $f(0)=0$,
$f(\beta) = \beta, \ f(s) < s$ for $s\in (0,\beta), \ f(s) > s$ for $s \in (\beta, \infty)$ and $f'(\beta)>\lambda^{r}_k$.
D. Bonheure, B. Noris and T. Weth [Ann. Inst. H. Poincaré Anal. Non Linéaire 29(4) (2012)] proved the existence of nondecreasing, radial positive solutions of the semilinear Neumann problem
$$
-\Delta u+u=f(u) \ \text{in}\ B_1,\ \ \ \ \partial_\nu u=0 \ \text{on}\ \partial B_1
$$
for $k=2$, and they conjectured that there exists a radial solution with $k$ intersections with $\beta$ provided that $f'(\beta) >\lambda^r_k$ for $k>2$, where $\lambda^r_k$ is the $k$-th radial eigenvalue of $\Delta + I$ in the unit ball with Neumann boundary conditions. In this paper, we show that the answer is yes in the case of linearly bounded nonlinearities.

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