Nonexistence of homoclinic orbits for a class of Hamiltonian systems
type: Item
instance of: scholarly article
title: Nonexistence of homoclinic orbits for a class of Hamiltonian systems
zbMATH Open document ID: 1296.34120
DOI: 10.1155/2013/547682
author: Xiaoyan Lin
author: Qi-Ming Zhang
author: X. H. Tang
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We give several sufficient conditions under which the first-order nonlinear Hamiltonian system \[ x'(t)= \alpha(t) x(t)+ f(t, y(t)),\quad y'(t)=-g(t, x(t))- \alpha(t) y(t) \] has no solution \((x(t),y(t))\) satisfying condition \[ 0< \int^{+\infty}_{-\infty} [|x(t)|^\nu+ (1+ \beta(t))|y(t)|^\mu]\,dt< +\infty, \] where \(\mu,\nu>1\) and \((1/\mu)+ (1/\nu)= 1\), \(0\leq xf((t,x)\leq \beta(t)|x|^\mu\), \(xg(t,x)\leq \gamma_0(t)|x|^\nu\), \(\beta(t)\), \(\gamma_0(t)\geq 0\), and \(\alpha(t)\) are locally Lebesgue integrable real-valued functions defined on \(\mathbb{R}\).
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 6306994
Wikidata QID: Q58917099
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/547682
OpenAlex ID: W2136811798
cites work: Multiple homoclinic orbits for a class of conservative systems
cites work: Dual variational methods in critical point theory and applications
cites work: A variational approach to homoclinic orbits in Hamiltonian systems
cites work: Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials
cites work: Existence of infinitely many homoclinic orbits in Hamiltonian systems
cites work: Q3837541
cites work: Homoclinic orbits for a nonperiodic Hamiltonian system
cites work: Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system
cites work: The existence of homoclinic orbits for Hamiltonian systems with the potentials changing sign
cites work: Homoclinic solutions for a class of the second order Hamiltonian systems
cites work: Existence of even homoclinic orbits for second-order Hamiltonian systems
cites work: Homoclinic orbits for a class of Hamiltonian systems
cites work: Some results on connecting orbits for a class of Hamiltonian systems
cites work: Homoclinic orbits for asymptotically linear Hamiltonian systems
cites work: Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits
cites work: Homoclinic solutions for a class of second-order Hamiltonian systems
cites work: Infinitely many homoclinic orbits for Hamiltonian systems with indefinite sign subquadratic potentials
cites work: Lyapunov inequalities and stability for linear Hamiltonian systems
cites work: Lyapunov-type inequalities for the first-order nonlinear Hamiltonian systems
cites work: A Lyapunov Inequality for a Certain Second Order Non-Linear Differential Equation
cites work: Lyapunov Type Inequalities for Certain Second Order Functional Differential Equations
cites work: Lyapunov inequalities for discrete linear Hamiltonian systems
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description: scientific article; zbMATH DE number 6306994