Results 41 to 50 of about 14,168 (160)
Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems
Advances in Difference Equations, 2007 An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.
Bo Zheng
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Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems
Abstract and Applied Analysis, 2013 We establish a new existence result on homoclinic solutions for a second-order nonperiodic Hamiltonian systems. This homoclinic solution is obtained as a limit of solutions of a certain sequence of nil-boundary value problems which are obtained by the ...
Qiang Zheng
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Survey of Eight Modern Methods of Hamiltonian Mechanics
Axioms, 2021 Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them.
Alexander D. Bruno, Alexander B. Batkhin
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Frontiers in Applied Mathematics and Statistics, 2023 We discuss structure-preserving model order reduction for port-Hamiltonian systems based on a nonlinear approximation ansatz which is linear with respect to a part of the state variables of the reduced-order model.
Philipp Schulze
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On stability zones for discrete-time periodic linear Hamiltonian systems
Advances in Difference Equations, 2006 The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuous-time version, these results go back to Liapunov and Žukovskii; their deep
Răsvan Vladimir
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On Oscillation Properties for Linear Hamiltonian Systems
Rocky Mountain Journal of Mathematics, 2009 The authors investigate oscillatory properties of the linear Hamiltonian differential system \[ x'=A(t)x+B(t)u,\quad u'=C(t)x-A^*(t)u \tag{*} \] under the assumption that the matrix \(B\) is positive definite. The main result of the paper is a statement showing that (*) is oscillatory provided \(\limsup\) of the largest eigenvalue of a certain ...
Zheng, Zhaowen, Meng, Fanwei
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Interval criteria for oscillationof linear Hamiltonian systems
Mathematical and Computer Modelling, 2004 The authors consider the linear matrix Hamiltonian system \[ X'=A(t)X+B(t)Y,\quad Y'=C(t)X-A^*(t)Y,\quad t\geq t_0, \] where \(X(t), Y(t), A(t), B(t)=B^*(t)>0\) and \(C(t)=C^*(t)\) are \(n\times n\)-matrices whose entries real-valued continuous functions. By employing the substitution \(W(t)=a(t)[Y(t)X^{-1}(t)+f(t)B^{-1}(t)]\) and a fundamental matrix \
Fanwei Meng, Yuangong Sun
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Crossing Limit Cycles of Planar Piecewise Linear Hamiltonian Systems without Equilibrium Points
Mathematics, 2020 In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if ...
Rebiha Benterki, Jaume LLibre
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Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation
Boundary Value Problems, 2010 We investigate the existence of periodic solutions of linear Hamiltonian systems with a nonlinear perturbation. Under generalized Ahmad-Lazer-Paul type coercive conditions for the nonlinearity on the kernel of the linear part, existence of periodic ...
Zhiqing Han
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Nontrivial periodic solutions of asymptotically linear Hamiltonian systems
Electronic Journal of Differential Equations, 2001 We study the existence of periodic solutions for some asymptotically linear Hamiltonian systems. By using the Saddle Point Theorem and Conley index theory, we obtain new results under asymptotically linear conditions.
Guihua Fei
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