Infinitely many periodic solutions to a class of perturbed second-order impulsive Hamiltonian systems
Copyright policy )Infinitely many periodic solutions to a class of perturbed second-order impulsive Hamiltonian systems
From the introduction and summary: The aim of this paper is to investigate the existence of infinitely many periodic \[ \begin{gathered} -\ddot u(t)+ A(t) w(t)=\lambda\nabla F(t,u(t))+ \mu\nabla G(t,u(t))+\nabla H(u(t)),\quad \text{a.e. }t\in [0,T],\\ \Delta(\dot u_j(t_j))= I_{ij}(u_i(t_j)),\quad i= 1,2,\dots, N,\;j=1,2,\dots, p,\\ u(0)= u(T)=\dot u(0)-\dot u(T)= 0,\end{gathered} \] where \(u= (u_1,u_2,\dots, u_N)^{{\mathcal I}}\) (transpose), \(N\geq 1\), \(p>1\), \(T>0\), \(\lambda>0\) and \(\mu\geq 0\) are parameters, \(0= t_0
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, perturbed Hamiltonian systems, infinitely many solutions, Nonlinear spectral theory, nonlinear eigenvalue problems, Parameter dependent boundary value problems for ordinary differential equations, critical point theory, Applications of variational problems in infinite-dimensional spaces to the sciences, impulsive systems, variational methods, periodic solutions, Periodic solutions to ordinary differential equations
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, perturbed Hamiltonian systems, infinitely many solutions, Nonlinear spectral theory, nonlinear eigenvalue problems, Parameter dependent boundary value problems for ordinary differential equations, critical point theory, Applications of variational problems in infinite-dimensional spaces to the sciences, impulsive systems, variational methods, periodic solutions, Periodic solutions to ordinary differential equations
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