Variational approach to a class of second order Hamiltonian systems on time scales

DOI10.1007/S10440-011-9649-ZzbMath1238.34159OpenAlexW1992518298MaRDI QIDQ663436

Jianwen Zhou, Li Yong Kun

Publication date: 15 February 2012

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-011-9649-z

zbMATH Keywords

time scalesHamiltonian systemscritical pointsvariational approach

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Dynamic equations on time scales or measure chains (34N05)

Related Items (8)

Existence and exponential stability of periodic solutions for a class of Hamiltonian systems on time scales ⋮ Variational approach to a class of \(p\)-Laplacian systems on time scales ⋮ Variational approach of \(p\)-Laplacian impulsive differential equations with periodic conditions ⋮ Variational approach to second-order impulsive dynamic equations on time scales ⋮ An application of variational approach to a class of damped vibration problems with impulsive effects on time scales ⋮ Variational approach for a p-Laplacian boundary value problem on time scales ⋮ Multiple positive solutions of nonlinear third-order boundary value problems with integral boundary conditions on time scales ⋮ Fractional Sobolev space on time scales and its application to a fractional boundary value problem on time scales

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Periodic solutions for a class of non-autonomous Hamiltonian systems
• Existence of solutions for a class of damped vibration problems on time scales
• Existence of positive periodic solutions for functional differential equations with impulse effects on time scales
• Analysis on measure chains - a unified approach to continuous and discrete calculus
• Existence of positive solutions for singular boundary value problem on time scales
• Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales
• Sobolev's spaces on time scales and its applications to a class of second order Hamiltonian systems on time scales
• Critical point theory and Hamiltonian systems
• Basic calculus on time scales and some of its applications
• Integration on time scales.
• Existence theory for positive solutions to one-dimensional \(p\)-Laplacian boundary value problems on time scales
• Existence and approximation of extremal solutions to first-order infinite systems of functional dynamic equations
• Basic properties of Sobolev's spaces on time scales
• Periodic solutions for a neutral nonlinear dynamical equation on a time scale
• Eigenfunction expansions in \(L^{2}\) spaces for boundary value problems on time-scales
• Deformation theorems on non-metrizable vector spaces and applications to critical point theory

This page was built for publication: Variational approach to a class of second order Hamiltonian systems on time scales