Results 31 to 40 of about 1,359 (222)

Infinite Homoclinic Solutions of the Discrete Partial Mean Curvature Problem with Unbounded Potential

Mathematics, 2022
The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons.
Yanshan Chen, Zhan Zhou
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Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge. [PDF]

Quant Biol
Abstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Zhang P, Gao T, Guo J, Duan J.
europepmc   +2 more sources

Homoclinic and heteroclinic solutions to a hepatitis C evolution model

Open Mathematics, 2018
Homoclinic and heteroclinic solutions to a standard hepatitis C virus (HCV) evolution model described by T. C. Reluga, H. Dahari and A. S. Perelson, (SIAM J. Appl. Math., 69 (2009), pp. 999–1023) are considered in this paper.
Telksnys Tadas, Navickas Zenonas, Marcinkevicius Romas, Cao Maosen, Ragulskis Minvydas   +4 more
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Novel Hyperbolic Homoclinic Solutions of the Helmholtz-Duffing Oscillators

Shock and Vibration, 2016
The exact and explicit homoclinic solution of the undamped Helmholtz-Duffing oscillator is derived by a presented hyperbolic function balance procedure.
Yang-Yang Chen, Shu-Hui Chen, Wei-Wei Wang   +2 more
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Homoclinic Solutions of Hamiltonian Systems with Symmetry

Journal of Differential Equations, 1999
Consider a Hamiltonian system with a Hamiltonian of the following form: \[ H(z,t)=\tfrac{1}{2}Az\cdot z+F(z,t). \] The authors show that if (i) the spectrum of the matrix \(JA\) (where \(J\) is the standard symplectic matrix) does not intersect the imaginary axis; (ii) \(F\) is invariant under the action of a compact Lie group; and (iii) \(F\) is ...
ARIOLI, GIANNI, A. Szulkin
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On Existence of Infinitely Many Homoclinic Solutions

Monatshefte f�r Mathematik, 2000
Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation ...
Wójcik, Klaudiusz, Zgliczyński, Piotr
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Infinitely many homoclinic solutions for a class of damped vibration problems

Electronic Journal of Qualitative Theory of Differential Equations, 2022
In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems $$ \ddot{x}(t)+B\dot{x}(t)-A(t)x(t)+H_{x}(t,x(t))=0,$$ where $A(t)\in (\mathbb{R},\mathbb{R}^{N})$ is a symmetric matrix for all $t\in \mathbb{
Huijuan Xu, Shan Jiang, Guanggang Liu
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Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems

Abstract and Applied Analysis, 2013
We establish a new existence result on homoclinic solutions for a second-order nonperiodic Hamiltonian systems. This homoclinic solution is obtained as a limit of solutions of a certain sequence of nil-boundary value problems which are obtained by the ...
Qiang Zheng
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Homoclinic Solutions for Fourth Order Traveling Wave Equations [PDF]

SIAM Journal on Mathematical Analysis, 2009
We consider homoclinic solutions of fourth order equations $$ u^{""} + β^2 u^{"} + V_u (u)=0 {in} \R ,$$ where $V(u)$ is either the suspension bridge type $V(u)=e^u-1-u$ or Swift-Hohenberg type $ V(u)= {1/4}(u^2-1)^2$. For the suspension bridge type equation, we prove existence of a homoclinic solution for {\em all} $ β\in (0, β_*)$ where $ β_{*}= 0 ...
Sanjiban Santra, Juncheng Wei
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Multiple transverse homoclinic solutions near a degenerate homoclinic orbit

Journal of Differential Equations, 2015
The authors study periodic perturbations of differential equations possessing a degenerate homoclinic orbit. Regarding the degeneracy it is assumed more precisely that along the homoclinic orbit the tangent spaces of the corresponding stable and unstable manifolds intersect in a two-dimensional space.
Lin, Xiao-Biao, Long, Bin, Zhu, Changrong   +2 more
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