Results 11 to 20 of about 2,741,766 (204)
Homoclinic and quasi-homoclinic solutions for damped differential equations
Electronic Journal of Differential Equations, 2015 We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \ddot{u}+c\dot{u}-L(t)u+W_u(t,u)=0, $$ where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on
Chuan-Fang Zhang, Zhi-Qing Han
doaj +3 more sources
Existence and multiplicity of homoclinic solutions for a difference equation
Electronic Journal of Differential Equations, 2020 The aim of this article is to obtain homoclinic solutions for a discrete problem involving p-Laplacian. We prove the existence of at least one, two and three solutions for the problem. Our approach is based on variational methods.
Shapour Heidarkhani +2 more
doaj +7 more sources
Center Manifolds for Homoclinic Solutions [PDF]
Journal of Dynamics and Differential Equations, 2000 Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
Sandstede, Björn
core +4 more sources
Homoclinic Solutions of Hamiltonian Systems with Symmetry [PDF]
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
openaire +3 more sources
Existence problems for homoclinic solutions
Abstract and Applied Analysis, 2002 The problem x˙=f(t,x), x(−∞)=x(+∞), where x(±∞):=limt→±∞x(t)∈ℝn, is considered. Some existence results for this problem are established using the fixed point method and topological degree theory.
Cezar Avramescu
doaj +4 more sources
Homoclinic Solutions of an Integral Equation: Existence and Stability [PDF]
Journal of Differential Equations, 1999 The authors study (stationary) evolution equation in the form of the following nonlinear convolution type integral equation \[ (J\ast u)(x)- u(x)-f[u(x)]=0,\tag{1} \] with the condition \(u(\pm \infty)=0.\) It is assumed, that \(J(z)\geq 0\), \(\int J(z) dz =1\) and \(f\) is bistable. They construct homoclinic (even) solutions to the equation (1).
Chmaj, Adam, Ren, Xiaofeng
openaire +3 more sources
Homoclinic solutions for Hamiltonian system with impulsive effects
Advances in Difference Equations, 2018 In this article, we investigate a class of impulsive Hamiltonian systems with a p-Laplacian operator. By establishing a series of new sufficient conditions, the existence of homoclinic solutions to such type of systems is revealed.
Jian Liu +3 more
doaj +2 more sources
Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits [PDF]
, 2008 In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear
Waters, Thomas +3 more
core +4 more sources
Multiple bursting patterns in lateral habenula neurons: Experiments and computational model. [PDF]
J PhysiolAbstract figure legend LHb neurons display a variety of bursting patterns, as well as being silent or displaying a tonic or irregular firing pattern. In a set of patch‐clamp experiments in ex vivo mouse lateral habenula (LHb), we were able to record from a number of cells showing characteristic bursts of a few distinguishable types.
Fedorov D +5 more
europepmc +2 more sources
Global Continuation of Homoclinic Solutions [PDF]
Zeitschrift für Analysis und ihre Anwendungen, 2018 When extending bifurcation theory of dynamical systems to nonautonomous problems, it is a central observation that hyperbolic equilibria persist as bounded entire solutions under small temporally varying perturbations. In this paper, we abandon the smallness assumption and aim to investigate the global structure of the entity of all such bounded entire
Potzsche, Christian, Skiba, Robert
openaire +2 more sources