Differential Equations and Dynamical Systems
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Synchronization of Stochastic Fuzzy Cellular Neural Networks with Leakage Delay Based on Adaptive Control
Differential Equations and Dynamical Systems - Tập 22 - Trang 319-332 - 2013
This paper considers the synchronization problem of coupled chaotic fuzzy
cellular neural networks with stochastic noise perturbation and time delay in
the leakage term by using adaptive feedback control. Motivated by the
achievements from both the stability of neural networks with time delay in the
leakage term and the synchronization of coupled chaotic fuzzy cellular neural
networks with stochas...
Oscillation of third order nonlinear functional dynamic equations on time scales
Differential Equations and Dynamical Systems - Tập 18 - Trang 199-227 - 2010
It is the purpose of this paper to give oscillation criteria for the third order
nonlinear functional dynamic equation $$ \left( {a\left( t \right)\left[ {\left(
{r\left( t \right)x^\Delta \left( t \right)} \right)^\Delta } \right]^\gamma }
\right)^\Delta + f\left( {t,x\left( {g\left( t \right)} \right)} \right) = 0 $$
on a time scale $$ \mathbb{T} $$ , where γ is the quotient of odd positive
inte...
Linearized Stability for a New Class of Neutral Equations with State-Dependent Delay
Differential Equations and Dynamical Systems - Tập 24 - Trang 63-79 - 2014
For neutral delay differential equations of the form $$\begin{aligned}
\dot{x}(t)=g(\partial x_t,x_t), \end{aligned}$$ with $$g$$ defined on an open
subset of the space $$C([-h,0],\mathbb {R}^n)\times C^1([-h,0],\mathbb {R}^n)$$
, we extend an earlier principle of linearized stability. The present result
applies to a wider class of neutral differential equations $$\begin{aligned}
\dot{x}(t) = f(x(...
Well-posedness and Energy Decay of Solutions to a Nonlinear Bresse System with Delay Terms
Differential Equations and Dynamical Systems - Tập 28 - Trang 447-478 - 2016
We consider the Bresse system in bounded domain with delay terms in the
nonlinear internal feedbacks $$\begin{aligned} \left\{ {\begin{array}{l}\rho
_{1}\varphi _{tt}-Gh (\varphi _{x}+\psi +l\omega )_{x}-lEh(\omega _{x}-l\varphi
)+\mu _{1}g_1(\varphi _{t}(x,t)) +\mu _{2}g_2(\varphi _{t}(x,t-\tau _{1}))=0\\
\rho _{2}\psi _{tt}-EI\psi _{xx}+Gh(\varphi _{x}+\psi +l\omega ) +\widetilde{\mu
_{1}}\widet...
Infinitely Many Solutions for a Nonlinear Elliptic PDE with Multiple Hardy–Sobolev Critical Exponents
Differential Equations and Dynamical Systems - - Trang 1-21 - 2023
In this paper, by an approximating argument, we obtain two disjoint and infinite
sets of solutions for the following elliptic equation with multiple
Hardy–Sobolev critical exponents $$\begin{aligned} \left\{ \begin{array}{ll}
-\Delta u=\mu \vert u \vert ^{2^{*}-2} u + \sum _{i=1}^{l} \frac{ \vert u \vert
^{2^{*}(s_{i})-2}u}{ \vert x \vert ^{s_{i}}}+ a(x) \vert u \vert ^{q-2} u &{} \;
in \; \Omega ...
Pullback Attractors for a Nonlocal Nonautonomous Evolution Model in $$\mathbb {R}^N$$
Differential Equations and Dynamical Systems - Tập 28 Số 1 - Trang 87-105 - 2020
In this work we consider the nonlocal evolution equation with time-dependent
terms which arises in models of phase separation in $$\mathbb
{R}^N$$$$\begin{aligned} \partial _t u=- u + g \left( \beta (J*u) +\beta
h(t)\right) \end{aligned}$$under some restrictions on h, growth restrictions on
the nonlinear term g and $$\beta >1$$. We prove the existence, regularity and
upper-semicontinuity of pullba...
Exact Solutions of the Modified Benjamin–Bona–Mahoney (mBBM) Equation by Using the First Integral Method
Differential Equations and Dynamical Systems - Tập 21 - Trang 199-204 - 2012
In this paper, the first integral method is used to construct exact solutions of
the modified Benjamin–Bona–Mahoney (mBBM) equation. This method can be applied
to non-integrable equations as well as to integrable ones. By means of this
method, some exact solutions of mBBM equations are formally obtained. Obtained
results clearly indicate the reliability and efficiency of the first integral
method.
Whether chaos can be achieved in piecewise linear boundary value problems
Differential Equations and Dynamical Systems - Tập 18 - Trang 1-9 - 2010
We show that chaos in piecewise linear partial differential equations with
linear boundary conditions is realizable: even the simplest boundary value
problems of this kind can possess chaotic solutions in an open region of the
parameter space.
On the Controllability of Some Nonlinear Partial Functional Integrodifferential Equations with Finite Delay in Banach Spaces
Differential Equations and Dynamical Systems - Tập 29 - Trang 673-688 - 2017
This work concerns the study of the controllability for some nonlinear partial
functional integrodifferential equation with finite delay arising in the
modelling of materials with memory in Banach spaces. We give sufficient
conditions that ensure the controllability of the system by supposing that its
undelayed part admits a resolvent operator in the sense of Grimmer, and by
making use of the meas...
The Nonexistence of Positive Solutions for A Coupled System of Non-separated Boundary Value Problems
Differential Equations and Dynamical Systems - Tập 31 - Trang 1-15 - 2019
In this paper, we consider the non-separated boundary value problem for system
of nonlinear Riemann–Liouville fractional differential equations
$$\begin{aligned} \begin{aligned} D_{0^+}^{\alpha }x(t)+\lambda f(t, x(t),
y(t))=0,~~0...
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