Results 11 to 20 of about 864 (203)
Homoclinic Solutions for a Class of Nonlinear Difference Equations [PDF]
Journal of Applied Mathematics, 2014 We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach.
Ali Mai, Zhan Zhou
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Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems [PDF]
Journal of Applied Mathematics, 2012 A class of first-order noncoercive discrete Hamiltonian systems are considered. Based on a generalized mountain pass theorem, some existence results of homoclinic orbits are obtained when the discrete Hamiltonian system is not periodical and need not ...
Long Yuhua
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Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems [PDF]
Abstract and Applied Analysis, 2012 We study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum.
Wenping Qin, Jian Zhang, Fukun Zhao
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Newhouse phenomenon and homoclinic classes [PDF]
Ergodic Theory and Dynamical Systems, 2010 AbstractWe show that for a C1 generic subset of diffeomorphisms far from homoclinic tangencies, any infinite sequence of sinks or sources must accumulate on a homoclinic class of some saddle point with codimension one.
JIAGANG YANG
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Multiple homoclinic solutions for a class of nonhomogeneous Hamiltonian systems
Boundary Value Problems, 2018 By introducing a new superquadratic condition, we obtain the existence of two nontrivial homoclinic solutions for a class of perturbed second order Hamiltonian systems which are obtained by the mountain pass theorem and Ekeland’s variational principle.
Chunhua Deng, Dong-Lun Wu
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Periodic points and homoclinic classes [PDF]
Ergodic Theory and Dynamical Systems, 2006 We prove that there is a residual subset $\mathcal{I}$ of ${\rm Diff}^1({\it M})$ such that any homoclinic class of a diffeomorphism $f\in \mathcal{I}$ having saddles of indices $\alpha$ and $\beta$ contains a dense subset of saddles of index $\tau$ for every $\tau\in [\alpha,\beta]\cap \mathbb{N}$.
Abdenur, Flavio +4 more
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Homoclinic Solutions for a Class of the Second-Order Impulsive Hamiltonian Systems [PDF]
Abstract and Applied Analysis, 2013 This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a 2kT-periodic approximation solution is a ...
Jingli Xie, Zhiguo Luo, Guoping Chen
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Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we
Dong-Lun Wu
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Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems [PDF]
Abstract and Applied Analysis, 2013 We give several sufficient conditions under which the first-order nonlinear Hamiltonian system x'(t)=α(t)x(t)+f(t,y(t)), y'(t)=-g(t,x(t))-α(t)y(t) has no solution (x(t),y(t)) satisfying condition ...
Xiaoyan Lin, Qi-Ming Zhang, X. H. Tang
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Infinitely many homoclinic solutions for a class of nonlinear difference equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2012 By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee a class of nonlinear difference equation has infinitely many homoclinic orbits. Our conditions on the nonlinear term are rather relaxed and we generalize some
Peng Chen, Zhengmei Wang
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