Results 41 to 50 of about 7,276 (215)

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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Measure-expansive homoclinic classes

, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lee, Keonhee, Lee, Manseob
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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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Infinitely Many Homoclinic Solutions for Nonperiodic Fourth Order Differential Equations with General Potentials

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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Generic family with robustly infinitely many sinks [PDF]

, 2015
We show, for every $r>d\ge 0$ or $r=d\ge 2$, the existence of a Baire generic set of $C^d$-families of $C^r$-maps $(f_a)_{a\in (-1,1)^k}$ of a manifold $M$ of dimension $\ge 2$, so that for every $a$ small the map $f_a$ has infinitely many sinks.
Berger, Pierre
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Generic bi-Lyapunov stable homoclinic classes [PDF]

Nonlinearity, 2010
We study, for $C^1$ generic diffeomorphisms, homoclinic classes which are Lyapunov stable both for backward and forward iterations. We prove they must admit a dominated splitting and show that under some hypothesis they must be the whole manifold. As a consequence of our results we also prove that in dimension 2 the class must be the whole manifold and
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Classification and stability of simple homoclinic cycles in R^5

, 2012
The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple homoclinic cycle.
Brannath W, Conway J H, Du Val P, Guckenheimer J, Kirk V, Krupa M, Lauterbach R Matthews P, Melbourne I, Olga Podvigina, Podvigina O M, Podvigina O M, Podvigina O M, Postlethwaite C M, Sottocornola N, Ura T   +14 more
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A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations [PDF]

, 2011
The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$.
Abraham R., Angenent S. B., Angenent S. B., Angenent S. B., Anosov D. V., Arroyo A., Bendixson I., Bonatti C., Bonatti C., Bonatti C., Brunovský P., Brunovský P., Brunovský P., Brunovský P., Chen X.-Y., Crovisier S., Czaja R., Dancer E. N., Fiedler B., Fiedler B., Fiedler B., Fiedler B., Fiedler B., Fusco G., Fusco G., Fusco G., Fusco G., Galaktianov V. A., GENEVIÈVE RAUGEL, Ghrist R. W., Guckenheimer J., Hale J. K., Hale J. K., Hardt R., Hayashi S., Henry D., Henry D. B., Hirsch M. W., Hirsch M. W., Hirsch M. W., Hirsch M. W., Jolly M., Joly R., Joly R., Joly R., Mallet-Paret J., Matano H., Matano H., Matano H., Newhouse S. E., Nickel K., Nitecki Z., Palis J., Peixoto M. M., Peixoto M. M., Poláčik P., Poláčik P., Poláčik P., Poláčik P., Prizzi M., Pugh C. C., Pugh C. C., Pugh C. C., Pujals E. R., Robinson C., Robinson J. C., Rocha C., Rocha C., ROMAIN JOLY, Ruelle D., Sandstede B., Smale S., Smale S., Smale S., Smale S., Smillie J., Smith H. L., Smith H. L., Sturm C., Wolfrum M.   +79 more
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Homoclinics for singular strong force Lagrangian systems

Advances in Nonlinear Analysis, 2019
We study the existence of homoclinic solutions for a class of Lagrangian systems ddt$\begin{array}{} \frac{d}{dt} \end{array} $(∇Φ(u̇(t))) + ∇uV(t, u(t)) = 0, where t ∈ ℝ, Φ : ℝ2 → [0, ∞) is a G-function in the sense of Trudinger, V : ℝ × (ℝ2 ∖ {ξ}) → ℝ ...
Izydorek Marek, Janczewska Joanna, Mawhin Jean   +2 more
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Frequency spanning homoclinic families

, 2003
A family of maps or flows depending on a parameter $\nu$ which varies in an interval, spans a certain property if along the interval this property depends continuously on the parameter and achieves some asymptotic values along it. We consider families of
Arnold, Channon, Easton, Elskens, Gelfreich, Guckenheimer, Haberman, Henrard, Kaper, MacKay, Meiss, Meiss, Neishtadt, Neishtadt, Neı̆shtadt, Poincaré, Rom-Kedar, Rom-Kedar, Soto-Trevinõ, Tennyson, Treschev, Vered Rom-Kedar   +21 more
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