Second order Hamiltonian equations on T ∞ and almost-periodic
inﬁnite dimensions of second order Hamiltonian equations of the type jé=5rV,. [. rell” ... we construct uncountably many almost-periodic solutions for the inﬁnite.
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Second Order Hamiltonian Equations on T∞ and Almost-Periodic
May 25, 2002 ... Second Order Hamiltonian Equations on ... we construct uncountably many almost-periodic solutions for the infinite dimensional system ẍi ...
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On periodic solutions of second order Hamiltonian systems (I)
On periodic solutions of second order Hamiltonian systems (I) .... The parameter R and the period r(R) of x^(t) are related by the equation I-TW} 2rrR = r(R) X^t) dt. ..... This proviso is nearly self-evident, as J -r F(x(s)) ds is a functional in H whose ...
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The pendulum equation: from periodic to almost periodic forcings
The existence of almost periodic solutions has been already discussed in several papers by .... Going back to our second order equation (1) it is interesting to ...
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Some simple problems for the next generations
Dec 21, 2015 ... f : R −→ H be almost periodic and let u be a solution of de ... the smoothing effect provides some higher order regularity for t > 0 for ... is a second real Hilbert space H for which V ֒→ H = H′ ֒→ V .... There are in the Literature a lot of results on global behavior of solutions to Hamiltonian equations.
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Multibump homoclinic solutions for a class of second order, almost
Nonlinear Differential Equations and Applications NoDEA. Multibump homoclinic solutions for a class of second order, almost periodic Hamiltonian systems .... is a solution for any T ∈ R if α is constant and for any T = kT0, k ∈ N if α is T0.
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Existence and multiplicity of weak quasi-periodic solutions for
Zhang Advances in Difference Equations (2015) 2015:336 ... existence and multiplicity of weak quasi-periodic solutions for the second order Hamiltonian system d[P(t)˙u(t)] ... R and F(t,x) is almost periodic in t uniformly for x ∈ RN. When F has ...
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NONTRIVIAL PERIODIC SOLUTIONS TO SECOND-ORDER
Aug 10, 2015 ... Electronic Journal of Differential Equations, Vol. 2015 (2015), No ... solutions to the second-order impulsive Hamiltonian system. −ü(t) + ... differentiable in u for almost every t ∈ [0,T], F(t, 0,..., 0) = 0 for t ∈ [0,T], and satisfies the ...
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On the existence of almost periodic solutions for a class of - Hal
Jun 4, 2014 ... second order neutral delay differential equations u′′(t ... In order to study the almost periodic solutions of 1.1, we use, here, a variational formalism ...... Order Hamiltonian Systems Abstract and Applied Analysis, vol. 2012 ...
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Almost Periodic Solutions of the KdV Equation
of mathematical physics are completely integrable Hamiltonian systems. Included ... solutions of KdV which are periodic in x are almost periodic in t, ; .... polynomial inderivatives of u up to order ], such that for every periodic functionu .... We multiply the first equation by H on theright, the second by 0 on the right, and.
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HOMOCLINIC SOLUTIONS FOR A CLASS OF NONLINEAR
of solutions, such as periodic solutions, almost periodic solutions or ... of homoclinic solutions for first order or second order differential equations (see [1- 10] ... moclinic solutions for the following second-order Hamiltonian system x (t) ... homoclinic solutions to the following nonlinear second-order differential equation .
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Variational Methods for Almost Periodic Solutions of a Class of - Hal
Apr 30, 2009 ... tral delay equation to the almost periodic settings. ... Another special case of (1.1) is the following forced second-order neutral delay ......  J. Blot; Almost periodic solutions of forced second order Hamiltonian systems, Ann.
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On the construction of almost periodic solutions for a nonlinear
The second type of results concerns classical Hamiltonians of the form 'kinetic energy ... However, to find almost-periodic solutions one has to consider .... We rewrite the nonlinear Schrödinger equation as a Hamiltonian system in infinitely many .... is crucial in order to preserve the Lipschitz property B during the iterative ...
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Variational Approach to Quasi-Periodic Solution of Nonautonomous
May 18, 2011 ... Solution of Nonautonomous Second-Order. Hamiltonian Systems ... existence and uniqueness of almost periodic solution of 1.2 . ... A special case of the above equation is the system 1.1 ; our main purpose is to apply. Minmax ...
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Homoclinics for an Almost Periodically Forced Singular Hamiltonian
(a1) a(t) is a continuous almost periodic function of t with a(t) ≥ a0 > 0 for all t ∈ R. (W1) There ... the existence of homoclinic solutions for a Hamiltonian system of another type .... Consider the ordinary differential equation in E: (1.27) ......  K. Tanaka, Homoclinic orbits for a singular second order Hamiltonian system, Ann.
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Periodic Solutions of Non-Autonomous Second Order Hamiltonian
method and Rabinowtz's saddle point theorem to study the periodic solution when the ... Forced second order Hamiltonian systems, the forced pendulum equation, .....  Ortega R., The pendulum equation: from periodic to almost periodic ...
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HOMOCLINICS FOR AN ALMOST PERIODICALLY FORCED
the existence of homoclinic solutions for a Hamiltonian system of another type which was ... When a(t) is periodic, e.g. with period 1, and Q(t) is a homoclinic solution of (HS), then so is Q(t .... Consider the ordinary differential equation in E: (1.27) dη ds ...... solutions for almost periodic second order systems, preprint, 1994.
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HOMOGENIZATION OF DEGENERATE SECOND-ORDER PDE IN
Abstract. We study the homogenization of fully nonlinear degenerate second- order pde, ... In this note we consider the behavior, as ε → 0, of the solution uε ∈ BUC(RN ) of. (1.1) .... A is almost periodic with respect to y locally uniformly in p . ..... [LPV] were the first to consider the homogenization of Hamilton-Jacobi equations.
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periodic solutions of second order hamiltonian systems bifurcating
The goal of this article is to study closed connected sets of periodic solutions, of autonomous second order Hamiltonian systems, emanating from infinity. ... considered asymptotically linear equation of the form x(t) = A(λ)x(t)+a(x, λ), where the ...... KB, KA ∩ KB = ∅ and KA ∪ KB = K. Note that almost all (unk ,λ+) ∈ KB.
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Parametrically excited Hamiltonian partial differential equations
A careful expansion and analysis to second order in the perturbation .... This equation has a solution in the class of almost periodic solutions of t with values.
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