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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 11
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 11, Issue 2, June 2004
  4. Non-collision periodic solutions for singular Hamiltonian systems
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 11, Issue 4, December 2004
Nonlinear Differential Equations and Applications NoDEA : Volume 11, Issue 3, September 2004
Nonlinear Differential Equations and Applications NoDEA : Volume 11, Issue 2, June 2004
Externality and Hamilton-Jacobi equations
Differential equations with bounded positive Green’s functions and generalized Aizerman’s hypothesis
On rate-independent hysteresis models
On a class of degenerate potential elliptic system
Non-collision periodic solutions for singular Hamiltonian systems
Critical eigenvalues for a nonlinear problem
Multiple equilibria, periodic solutions and a priori bounds for solutions in superlinear parabolic problems
On the Fučík Spectrum of the p-Laplacian
Nonlinear Differential Equations and Applications NoDEA : Volume 11, Issue 1, February 2004
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Non-collision periodic solutions for singular Hamiltonian systems

Content Provider SpringerLink
Author Boughariou, Morched
Copyright Year 2004
Abstract We study the existence of classical (non-collision) T-periodic solutions of the Hamiltonian system $$\openup2pt \displaylines{ \dot q = H_p (t,p, q),\ \dot p = -H_q (t,p, q),\ p(t+T) = p(t),\quad q(t+T)=q(t),\ } $$ where $ p,q :{\bf R} \rightarrow {\bf R}^N (N \geq 3) $ and $ H (t,p,q) $ is a T-periodic function in t which has a singularity at $ q=0 $ like $ H(t,p,q)\sim {1 \over \beta}|p|^{\beta}-{1 \over |q|^{\alpha}} \hbox{ with }\; 0<\alpha < \beta \; \hbox{ and} \; \beta \geq 2. $ Under suitable conditions on H, we prove that if $\alpha \in ]{\beta \over 2}, \beta[$ then (HS) possesses at least one non-collision solution and if $\alpha \in ]0,{\beta \over 2}]$ then the generalized solution of (HS) obtained in [5] has at most one time of collision in its period.
Ending Page 223
Page Count 23
Starting Page 201
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 2
Volume Number 11
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2004-01-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword periodic solution non-collision Morse index Singular Hamiltonian system Asymptotic behavior of solutions Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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