## 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

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

Using penalization techniques and the Ljusternik-Schnirelmann theory, we establish the multiplicity and concentration of solutions for the following fractional Schrödinger equation

$\left\{ \begin{align} &{{\varepsilon }^{2\alpha }}{{\left( -\Delta \right)}^{a}}u+V\left( x \right)u=f\left( u \right),\ \ x\in {{\mathbb{R}}^{N}}, \\ &u\in {{H}^{a}}\left( {{\mathbb{R}}^{N}} \right),u>0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x\in {{\mathbb{R}}^{N}}, \\ \end{align} \right.$ |

where

,

,

is a small parameter,

satisfies the local condition, and

is superlinear and subcritical nonlinearity. We show that this equation has at least

single spike solutions.

$0<α<1$ |

$N>2α$ |

$\varepsilon>0$ |

$V$ |

$f$ |

$\text{cat}_{M_{δ}}(M)$ |

DCDS-S

In this paper we develop a non-autonomous reaction-diffusion model with the Robin boundary conditions to describe insect dispersal on an isotropically varying domain. We investigate the stability of the reaction-diffusion model. The stability results of the model describe either insect survival or vanishing.

keywords:
Stability
,
bifurcation
,
varying domain
,
insect dispersal model
,
Robin boundary condition

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

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

In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem from infinity for nonlinear operator equation with homogeneous operator. To deal with the superlinear case, we establish several topological results involving superior limit.

keywords:
superior limit
,
topological method.
,
Bifurcation
,
homogeneous operator
,
one-sign solution
,
$p$-Laplacian

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