Results 21 to 30 of about 8,851 (211)

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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Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology [PDF]

, 2006
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is
Kutafina, Ekaterina V., Pudelko, Anna, Vladimirov, Vsevolod A.   +2 more
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Existence and uniqueness of positive even homoclinic solutions for second order differential equations

Electronic Journal of Qualitative Theory of Differential Equations, 2019
This paper is concerned with the existence of positive even homoclinic solutions for the $p$-Laplacian equation \begin{equation*} (|u'|^{p-2}u')' - a(t)|u|^{p-2}u+f(t,u)=0,\qquad t\in \mathbb{R}, \end{equation*} where $p\ge 2$ and the functions $a ...
Adel Daouas, Monia Boujlida
doaj   +1 more source

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
doaj   +1 more source

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
openaire   +2 more sources

Multiple homoclinic solutions for a one-dimensional Schrödinger equation [PDF]

Discrete & Continuous Dynamical Systems - S, 2016
This paper is dedicated to the study of the problem of existence of homoclinic solutions to a Schrödinger equation of the form \[ x''-V(t)x+x^3=0,\eqno{(1)} \] where \(V:\mathbb R\to\mathbb R\) is a \(L^1\)-function.
DAMBROSIO, Walter, D. Papini
openaire   +3 more sources

Dynamics of Unilateral and Bilateral Control Systems with State Feedback for Renewable Resource Management

Complexity, 2020
In this paper, mathematical models for the management of biological resources based on a given predator-prey relationship are proposed, and two types of control strategies, unilateral and bilateral control with impulsive state feedback, are studied.
Mingzhan Huang, Shouzong Liu, Xinyu Song, Lansun Chen   +3 more
doaj   +1 more source

Twisted and Nontwisted Bifurcations Induced by Diffusion

, 1996
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop.
A. Lunardi, A. M. Turing, B. Deng, E. Conway, E. D. Conway, E. Yanagida, G. Prato Da, G. S. K. Wolkowicz, H. I. Freedman, H. Kokubu, J. Carr, J. D. Murray, J. K. Hale, L. P. Silnikov, P. C. Fife, P. Hartman, S.-N. Chow, S.-N. Chow, S.-N. Chow, S.-N. Chow, X. B. Lin, X. B. Lin, X. B. Lin, X.-B. Lin, X.-B. Lin, Xiao-Biao Lin   +25 more
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Homoclinic solutions for a class of non-periodic second order Hamiltonian systems

Electronic Journal of Qualitative Theory of Differential Equations, 2010
We study the existence of homoclinic solutions for the second order Hamiltonian system $\ddot{u}+V_{u}(t,u)=f(t)$. Let $V(t,u)=-K(t,u)+W(t,u)\in C^{1}(\mathbb{R}\times\mathbb{R}^{n}, \mathbb{R})$ be $T$-periodic in $t$, where $K$ is a quadratic growth ...
Jian Ding, Junxiang Xu, Fubao Zhang
doaj   +1 more source

Study of Stochastic–Fractional Drinfel’d–Sokolov–Wilson Equation for M-Shaped Rational, Homoclinic Breather, Periodic and Kink-Cross Rational Solutions

Mathematics, 2023
We explore stochastic–fractional Drinfel’d–Sokolov–Wilson (SFDSW) equations for some wave solutions such as the cross-kink rational wave solution, periodic cross-rational wave solution and homoclinic breather wave solution.
Shami A. M. Alsallami, Syed T. R. Rizvi, Aly R. Seadawy   +2 more
doaj   +1 more source