## 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

We discuss the existence of positive
solutions of perturbation to a class of quasilinear elliptic
equations on $\mathbb R$.

DCDS

In this paper, as bound state solutions we consider least energy sign-changing solutions to a nonlinear elliptic system
which consists of N-equations defined on a bounded domain $\Omega$.
For any subset $K\subset \{1,\cdots, N\}$,
we show the existence of sign-changing solution
$\vec{u}=(u_1,\cdots,u_n)$ such that,
for $i\in K$, $u_i$ are sign-changing functions that change sign exactly once
in $\Omega$,
and, for $i\notin K$, $u_i$ are one sign functions.
We give a variational characterization of such solutions on modified Nehari type constrained sets.

CPAA

We establish some imbedding results of weighted Sobolev spaces. The
results then are used to obtain ground state solutions of nonlinear
elliptic equations with anisotropic coefficients.

DCDS

Consider the following nonlinear elliptic system
\begin{equation*}
\left\{\begin{array}{ll}
-\Delta u - u=\mu_1u^3+\beta uv^2,\ & \hbox{in}\ \Omega\\
-\Delta v - v= \mu_2v^3+\beta vu^2,\ & \hbox{in}\ \Omega\\
u,v>0\ \hbox{in}\ \Omega, \ u=v=0,\ & \hbox{on}\ \partial\Omega,
\end{array}
\right.
\end{equation*}where $\mu_1,\mu_2>0$ are constants and $\Omega$ is a smooth bounded domain in
$\mathbb{R}^N$ for $N\leq3$. We study the existence and non-existence of
positive solutions and give bifurcation results in terms of the
coupling constant $\beta$.

DCDS

In this paper, we are interested in
the existence of
subharmonic solutions for the problem
$ u_{t t} + G'(u) = f(t), $
where $G:R^{ N} \rightarrow R$ is not necessarily convex and
$f:R \rightarrow R^N$ is periodic with minimal period $T > 0$.

PROC

Please refer to Full Text.

keywords:

CPAA

In this paper we obtain some existence and multiplicity results for periodic solutions of nonautonomous Hamiltonian
systems $\dot z(t)=J\nabla H(z(t),t)$ whose Hamiltonian functions may have simultaneously, in different components,
superquadratic, subquadratic and quadratic behaviors. Our results generalize some earlier work [3] of P. Felmer
and [5] of P. Felmer and Z.-Q. Wang.

CPAA

In this paper, we establish the existence of nontrivial ground-state solutions for a coupled nonlinear Schrödinger system

$-\Delta u_j+ u_j=\sum\limits_{i=1}^mb_{ij}u_i^2u_j, \quad\text{in}\ \mathbb{R}^n,\\ u_j(x)\to 0\ \text{as}\ |x|\ \to \infty, \quad j=1,2,\cdots, m,$ |

where $n=1, 2, 3, m\geq 2$ and $b_{ij}$ are positive constants satisfying $b_{ij}=b_{ji}.$ By nontrivial we mean a solution that has all components non-zero. Due to possible systems collapsing it is important to classify ground state solutions. For $m=3$, we get a complete picture that describes whether nontrivial ground-state solutions exist or not for all possible cases according to some algebraic conditions of the matrix $B = (b_{ij})$. In particular, there is a nontrivial ground-state solution provided that all coupling constants $b_{ij}, i\neq j$ are sufficiently large as opposed to cases in which any ground-state solution has at least a zero component when $b_{ij}, i\neq j$ are all sufficiently small. Moreover, we prove that any ground-state solution is synchronized when matrix $B=(b_{ij})$ is positive semi-definite.

DCDS

Two indices, which are similar to the Krasnoselski's genus on the
sphere, are defined on the product of spheres. They are applied to
investigate the multiple non semi-trivial solutions for elliptic
systems. Both constraint and unconstraint problems are studied.

DCDS-B

Electro-kinetic fluids can be modeled by
hydrodynamic systems
describing the coupling between fluids and electric charges.
The system
consists of a momentum equation together with transport equations
of charges. In the dynamics, the special coupling between
the Lorentz force in the velocity equation and the material transport
in the charge equation gives an energy dissipation law.
In stationary situations, the system reduces
to a Poisson-Boltzmann type of equation. In particular, under
the no flux boundary conditions, the conservation of the total charge
densities gives nonlocal integral terms in the equation.
In this paper, we analyze the qualitative properties of solutions
to such an equation, especially
when the Debye constant $\epsilon$ approaches zero.
Explicit properties can be derived for the one
dimensional case while some may be generalized to
higher dimensions.
We also present some numerical simulation results of the system.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]