Results 151 to 160 of about 636 (179)

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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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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Variational Approach to Homoclinic Solutions for Fractional Hamiltonian Systems

Journal of Optimization Theory and Applications, 2017
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Nemat Nyamoradi, Yong Zhou 0005, Bashir Ahmad 0003, Ahmed Alsaedi   +3 more
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Homoclinic and heteroclinic solutions of upheaval buckling

Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1997
Summary: Upheaval of a heavy flexible strut from a rigid bed is viewed as an initial value problem, and spatial kinetic and potential energy functions are consequently defined. Upheaval from a perfectly flat state is characterized by the simultaneous vanishing of both functions at the boundaries.
Hunt, G. W., Blackmore, A.
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Homoclinic Solutions for a Forced Liénard Type System

Results in Mathematics, 2009
The author investigates the existence of homoclinic solutions of the forced Liénard type system \[ \ddot{x}+F(\dot{x})+ g(x)=p(t), \] where \(F\) and \(g\) are continuous functions on \(\mathbb{R}\) and \(p\) is a bounded continuous function on \(\mathbb{R}\).
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Homoclinic solutions for a higher order difference equation

Applied Mathematics Letters, 2018
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Homoclinic solutions for a class of fourth‐order difference equations

Mathematical Methods in the Applied Sciences, 2015
In this paper, a class of fourth‐order nonlinear difference equation is considered. By making use of the critical point theory, we establish various sets of sufficient conditions for the existence of homoclinic solutions and give some new results. One of our results generalizes and improves the results in the literature.
Shi, Haiping, Liu, Xia, Zhang, Yuanbiao
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Fast homoclinic solutions for a class of damped vibration problems

Applied Mathematics and Computation, 2013
Authos' abstract: We deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problem \[ \ddot{u}(t) + q(t)\dot{u}(t) - L(t)u(t) + \nabla W(t, u(t)) = 0, \] where \(L(t)\) and \(W(t, x)\) are neither autonomous nor periodic in \(t\). Our approach is variational and it is based on the critical point theory.
Peng Chen 0003, Xianhua Tang, Ravi P. Agarwal   +2 more
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Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension

SIAM Journal on Mathematical Analysis, 1992
Two parameter families of autonomous differential equations are considered, and it is assumed that at the origin of the parameter plane the origin of the phase space is a saddle type equilibrium of the system with a homoclinic trajectory. Conditions are given under which there exist one or more curves in the parameter plane at the points of which the ...
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