Results 141 to 150 of about 636 (179)

Existence and Uniqueness of Homoclinic Solution for a Rayleigh Equation with a Singularity

Qualitative Theory of Dynamical Systems, 2020
By using a continuation theorem of coincidence degree principle, the authors give some new results on the existence and uniqueness of homoclinic solution for the following singular Rayleigh equation, \[ x''(t)+f(x'(t))-g(x(t))-\frac{\alpha(t)x(t)}{1-x(t)}=h(t), \] where $f,g,h,\alpha:\mathbb{R}\rightarrow\mathbb{R}$ are continuous functions.
Shiping Lu, Lu Shiping
exaly   +3 more sources

Homoclinic solutions for an anomalous diffusion system

Journal of Mathematical Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yanheng Ding, Qi Guo
exaly   +2 more sources

Homoclinic breather and rogue wave solutions to Maccari equation

Computers and Mathematics With Applications, 2020
The (2+1)-dimensional Maccari nonlinear system is given by \begin{align*} \mathrm{i}u_t+u_{xx}+u v & =0\\ v_t + v_y + (|u|^2)_x & =0, \end{align*} where \(u=u(x,y,t)\) and \(v=v(x,y,t)\) are, respectively, complex- and real-valued functions of the temporal variable \(t\) and the spatial variables \(x\) and \(y\).
Ying Jiang, Da-Quan Xian
exaly   +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 for ordinary p-Laplacian systems

Applied Mathematics and Computation, 2012
The authors study the ordinary \(p\)-Laplacian system \[ \frac{d}{dt}(\left|\dot{u}(t)\right|^{p-2}\dot{u}(t))+\nabla V(t,u(t))=f(t), \] where \(p> 1\), \(t\in\mathbb R\), \(u\in\mathbb R^{n}\) and \(V\in \mathbb C^{1}(\mathbb R\times\mathbb R^{n},\mathbb R)\), \(V(t,x)=-K(t,x)+W(t,x)\) is \(T\)-periodic with respect to \(t\), \(T>0\), and \(f:\mathbb ...
Xiang Lv, Shiping Lu
openaire   +1 more source

A Homoclinic Solution for Excitation Waves on a Contractile Substratum

SIAM Journal on Applied Dynamical Systems, 2012
We analyze a model of electric signaling in biological tissues and prove that this model admits a traveling wave solution. Our result is based on a new technique for computing rigorous bounds on the stable and unstable manifolds at an equilibrium point of a dynamical system depending on a parameter.
AMBROSI, DAVIDE CARLO, ARIOLI, GIANNI, H. Koch   +2 more
openaire   +2 more sources

Center Manifolds for Homoclinic Solutions

Journal of Dynamics and Differential Equations, 2000
Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
openaire   +2 more sources

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

Existence of Homoclinic Solutions for a Class of Damped Vibration Problems

Qualitative Theory of Dynamical Systems, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huijuan Xu, Shan Jiang, Guanggang Liu
openaire   +2 more sources

Homoclinic solutions for Davey-Stewartson equation

Chaos, Solitons & Fractals, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Jian, Dai, Zhengde
openaire   +2 more sources