Existence of homoclinic solutions for Hamiltonian systems
Advances in Differential Equations, 2002 Using variational methods, the existence of homoclinic solutions is shown for the Hamiltonian system \(Ju'(x)+Mu(x)-\nabla_uF(x,u(x))=\lambda u(x)\), where \(u : \mathbb{R}\to \mathbb{R}^{2N}\), \(J\), \(M\) are matrices such that \(J=-J^T=-J^{-1}\), \(M^T=M\) and \(F\) is a Carathéodory nonlinearity satisfying addition properties.
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On sequences of large homoclinic solutions for a difference equations on\n the integers involving oscillatory nonlinearities [PDF]
, 2016 Robert Stegliński
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Weak homoclinic solutions of anisotropic discrete nonlinear system with variable exponent [PDF]
, 2020 Idrissa Ibrango +3 more
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The Existence of Transverse Homoclinic Solutions for Higher Order Equations
Journal of Differential Equations, 1996 Parametrized differential equations of the form \(\dot x(t)=f(x(t),\mu,t)\), where \(x\in \mathbb{R}^n\), \(\mu\in \mathbb{R}^N\), are considered. It is assumed that \(f\) is of \(C^3\)-class, \(f(x,0,t)\) is independent of \(t\), for all sufficiently small \(|\mu|\), \(x=0\) is a hyperbolic equilibrium, \(f\) is periodic in \(t\), and there exists a ...
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Multibump solutions for an almost periodically forced singular Hamiltonian system
Electronic Journal of Differential Equations, 1995 existence of so-called multibump homoclinic solutions for a family of singular Hamiltonian systems in $R^2$ which are subjected to almost periodic forcing in time.
Paul H. Rabinowitz
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Homoclinic solutions for a class of neutral Duffing differential systems [PDF]
, 2014 Wenbin Chen
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Homoclinic solutions in periodic partial difference equations
Advances in Nonlinear AnalysisBy using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed ...
Mei Peng, Zhou Zhan, Yu Jianshe
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Existence of homoclinic solutions for difference equations on integers via variational method
, 2022 Maisam Boroun +2 more
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Fast homoclinic solutions for a class of ordinary p-Laplacian systems [PDF]
, 2015 Bo Du
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Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem
, 1997 Alan Champneys, Gabriel J. Lord
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