\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Multiplicity of homoclinic orbits in quasi-linear autonomous Lagrangian systems

Abstract Related Papers Cited by
  • The existence of at least two homoclinic orbits is proved by A. Ambrosetti and V. Coti Zelati (Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ. Padova, 89 (1993), 177-194) for autonomous Lagrangian systems

    $\ddot{q}+V'(q)=0, ~q\in C^2(\R,\R^m),~m\geq 2 $

    where $V:\R^m\rightarrow\R$ is a function of the form

    $ V(q)=-\frac{|q|^2}{2}+W(q) $

    with $W\in C^2(\R^m,\R)$ superquadratic, satisfying a "pinching'' hypothesis and an hypothesis on its second derivative.
       The present work deals with potentials of the form $W(q,\dot{q})$ that weakly depend on $\dot{q}$. In this case an homoclinic orbit corresponds to a classical solution to the equation

    $\ddot{q}-q+W_1(q,\dot{q})-\frac{d}{dt}W_2(q,\dot{q})=0,$

    where $W_i=\partial_i W$ for $i=1,2$.

    Mathematics Subject Classification: Primary: 37J45, 58E50.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(70) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return