Results 171 to 180 of about 9,595 (205)

Bifurcation of Homoclinic Solutions for Hamiltonian Systems

Zeitschrift für Analysis und ihre Anwendungen, 2002
We consider the Hamiltonian system Ju'(x) + Mu(x) – \bigtriangledown _u F(x,u(x)) = \lambda u(x). Using variational methods obtained by Stuart on the one hand and by Giacomoni and Jeanjean on the other, we get bifurcation results for homoclinic solutions by imposing ...
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Homoclinic solutions for fractional discrete Laplacian equations

Nonlinear Analysis, 2020
The authors consider connegative homoclinic solutions of fractional difference equation by the fractional discrete Laplacian with a positive parameter. The variational method is applied using the mountain-pass theorem. The main result Theorem 1.1 is proved in Section 3. The paper is complete and clearly written.
Xiang, Mingqi, Zhang, Binlin
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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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Homoclinic breather-wave solutions for Sine–Gordon equation

Communications in Nonlinear Science and Numerical Simulation, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dai, Zhengde, Xian, Daquan
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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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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 an anomalous diffusion system

Journal of Mathematical Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Yanheng, Guo, Qi
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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 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 in Bazykin’s Predator-Prey Model

The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2020
In this paper we derive an explicit second-order approximation of the homoclinic solutions in the Bazykin’s predator-prey model. The analytic solutions are compared with those obtained by numerical continuation.
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