Results 171 to 180 of about 8,851 (211)

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.
openaire   +2 more sources

The Existence of Homoclinic Solutions for Hyperbolic Equations

Journal of Applied Analysis, 1995
Summary: We present a new variational method general enough to treat the problem of the existence of homoclinic solutions for the following semilinear wave equation: \[ x_{tt} (t,y)-x_{yy} (t,y)+ g\bigl(t,y,x(t,y) \bigr)=0 \quad \text{for} \quad ...
Nowakowski, A., Rogowski, A.
openaire   +1 more source

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
openaire   +1 more source

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 ...
openaire   +1 more source

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
openaire   +2 more sources

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.
openaire   +1 more source

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
openaire   +2 more sources

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
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +1 more source