Results 91 to 100 of about 2,741,766 (204)
Journal of Applied Mathematics, 2012 The authors study the existence and uniqueness of a set with 2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a ...
Lijuan Chen, Shiping Lu
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Homoclinic solutions for second order Hamiltonian systems with general potentials near the origin
Electronic Journal of Qualitative Theory of Differential Equations, 2013 In this paper, we study the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems with general potentials near the origin. Recent results from the literature are generalized and significantly improved.
Qingye Zhang
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Abstract and Applied Analysis, 2014 We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.
Liu Yang
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Saddle-node bifurcations of multiple homoclinic solutions in ODES
Discrete and Continuous Dynamical Systems - B, 2017 The authors study periodic perturbations of differential equations possessing a homoclinic orbit along which the tangent spaces of the corresponding stable and unstable manifolds intersect in a three-dimensional space. This paper can be seen as a continuation of the work ``Multiple transverse homoclinic solutions near a degenerate homoclinic orbit ...
Lin, Xiao-Biao, Zhu, Changrong
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Multiple homoclinic solutions for a class of nonhomogeneous Hamiltonian systems
Boundary Value Problems, 2018 By introducing a new superquadratic condition, we obtain the existence of two nontrivial homoclinic solutions for a class of perturbed second order Hamiltonian systems which are obtained by the mountain pass theorem and Ekeland’s variational principle.
Chunhua Deng, Dong-Lun Wu
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 This paper is concerned with the existence of positive even homoclinic solutions for the $p$-Laplacian equation \begin{equation*} (|u'|^{p-2}u')' - a(t)|u|^{p-2}u+f(t,u)=0,\qquad t\in \mathbb{R}, \end{equation*} where $p\ge 2$ and the functions $a ...
Adel Daouas, Monia Boujlida
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Symmetric homoclinic solutions to the periodic orbits in the Michelson system
, 2006 The Michelson system [D. Michelson, Steady solutions of the Kuramoto–Sivashinsky equation , Physica D 19 (1986), 89–111] $x'''+x'+0.5x^2=c^2$ for the parameter value $c=1$ is investigated. It was proven in \cite{8} that the system possesses two odd
Wilczak, Daniel
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Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems [PDF]
Abstract and Applied Analysis, 2013 We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian systemΔx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n)has no solution(x(n),y(n))satisfying condition0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, whereμ,ν>1and1/μ+1/ν=1andα(n),β(n),andγ(n)are real-valued functions defined onℤ.
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Center manifolds for homoclinic solutions
, 1995 In this article, center-manifold theory for homoclinic solutions of ordinary differential equations or semilinear parabolic equations is developed. Here, a center manifold along a homoclinic orbit q(t) is a locally invariant manifold containing all ...
Sandstede, B. +1 more
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Existence and stability of multiple spot solutions for the gray-scott model in R^2 [PDF]
, 2005 We study the Gray-Scott model in a bounded two dimensional domain and establish the existence and stability of {\bf symmetric} and {\bf asymmetric} multiple spotty patterns. The Green's function and its derivatives together with two nonlocal eigenvalue
Winter, M +3 more
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