Results 181 to 190 of about 1,359 (222)

Homoclinic solutions for ordinary p-Laplacian systems

Applied Mathematics and Computation, 2012
The authors study the ordinary \(p\)-Laplacian system \[ \frac{d}{dt}(\left|\dot{u}(t)\right|^{p-2}\dot{u}(t))+\nabla V(t,u(t))=f(t), \] where \(p> 1\), \(t\in\mathbb R\), \(u\in\mathbb R^{n}\) and \(V\in \mathbb C^{1}(\mathbb R\times\mathbb R^{n},\mathbb R)\), \(V(t,x)=-K(t,x)+W(t,x)\) is \(T\)-periodic with respect to \(t\), \(T>0\), and \(f:\mathbb ...
Xiang Lv, Shiping Lu
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A Homoclinic Solution for Excitation Waves on a Contractile Substratum

SIAM Journal on Applied Dynamical Systems, 2012
We analyze a model of electric signaling in biological tissues and prove that this model admits a traveling wave solution. Our result is based on a new technique for computing rigorous bounds on the stable and unstable manifolds at an equilibrium point of a dynamical system depending on a parameter.
AMBROSI, DAVIDE CARLO, ARIOLI, GIANNI, H. Koch   +2 more
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Center Manifolds for Homoclinic Solutions

Journal of Dynamics and Differential Equations, 2000
Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
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Homoclinic solution and chaos in

Nonlinear Analysis: Theory, Methods & Applications, 1981
xf(x) 0 , is followed by a move in the opposite direction (i(t) < 0). However, there are equations (1, 2) which are closely related to applications, and where the negative feedback condition (3) is only true in a certain neighbourhood of x = 0.
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Existence of Homoclinic Solutions for a Class of Damped Vibration Problems

Qualitative Theory of Dynamical Systems, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huijuan Xu, Shan Jiang, Guanggang Liu
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Homoclinic solutions for Davey-Stewartson equation

Chaos, Solitons & Fractals, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Jian, Dai, Zhengde
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The Homoclinic Orbit Solution for Functional Equation

Communications in Theoretical Physics, 2002
In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform, and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equations too. And the solitary wave exists in generalized dynamical systems and functional systems.
Liu Shi-Da, Fu Zun-Tao, Liu Shi-Kuo, Ren Kui   +3 more
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Generic existence of nondegenerate homoclinic solutions

Lobachevskii Journal of Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Motreanu, D., Motreanu, V. V.
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Periodic and homoclinic solutions generated by impulses

Nonlinear Analysis: Real World Applications, 2011
The topic of interest is the following class of second order differential equations with impulses \[ \ddot{q}+V_q(t,q)=f(t),\qquad t \in (s_{k-1},s_k), \] \[ \Delta \dot{q}(s_k)= g_{k}(q(s_k)), \] where \(k \in \mathbb{Z}\), \(q \in \mathbb{R}^n\), \(\Delta \dot{q}(s_k)= \dot{q}(s_k^+)- \dot{q}(s_k^-)\), \(V_q(t,q)=\text{grad}_q V(t,q)\), \(g_k(q ...
Zhang, Hao, Li, Zhixiang
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Homoclinic Solutions of Differential Equations

2001
In recent years, starting with works of Bolotin [Bol], Coti-Zelati, Ekeland and Sere [CZES], Coti-Zelati & Rabinowitz [CZR1], [CZR2], Rabinowitz [Ra4], variational methods have been applied to study the existence of homoclinic and heteroclinic solutions of second-order equations and Hamiltonian systems.
Maria do Rosário Grossinho, Stepan Agop Tersian   +1 more
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