On the stability of a mixed functional equation deriving from additive, quadratic and cubic mappings

Wang, Li Guang; Xu, Kun; Liu, Qiu Wen

doi:10.1007/s10114-014-3335-9

Cited by 11 publications

(4 citation statements)

References 19 publications

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“…One can see Section 4 for more details about this example. There are plenty of works about the stability of all kinds of equations, one can refer to [16][17][18][19][20][21][22][23] for a detailed description. In particular, for quasiperiodic equations, in order to determine the type of stability of the equilibria of quasiperiodic Hamiltonian systems, the authors need to assume that the corresponding linearized system is reducible, and some conditions were added to the system after the reducibility.…”

Section: Journal Of Function Spaces Assumption 2 (Nondegeneracy Condmentioning

confidence: 99%

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

Xue

Zhao

2020

Journal of Function Spaces

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In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt is analytic quasiperiodic with respect to t, and ε is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small ε, the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as Qt. Applications to the Schrödinger equation are also given.

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Section: Journal Of Function Spaces Assumption 2 (Nondegeneracy Condmentioning

confidence: 99%

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

Xue

Zhao

2020

Journal of Function Spaces

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“…In [39], Wang et al obtained the general solution and investigated the Ulam stability problem for the following mixed additive, quadratic and cubic functional equation…”

Section: Introductionmentioning

confidence: 99%

Almost additive-quadratic-cubic mappings in modular spaces

Maghsoudi¹,

Bodaghi²,

Motlagh³

et al. 2019

Rev. Un. Mat. Argentina

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We introduce and obtain the general solution of a class of generalized mixed additive, quadratic and cubic functional equations. We investigate the stability of such modified functional equations in the modular space Xρ by applying the ∆ 2-condition and the Fatou property (in some results) on the modular function ρ. Furthermore, a counterexample for the even case (quadratic mapping) is presented.

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“…Compared with the existence of solutions, the study on the dynamical stability behaviors of such equations is more difficult, and the results are fewer in the literature. Here we refer the reader to [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients

Xue

Zhao

2018

Journal of Function Spaces

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In this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian system x˙=A+εQt,εx, ε∈0,ε0, where A is a constant matrix with possible multiple eigenvalues and Q(t,ε) is analytic quasi-periodic with respect to t. Under nonresonant conditions, it is proved that this system can be reduced to y˙=A⁎ε+εR⁎t,εy, ε∈0,ε⁎, where R⁎ is exponentially small in ε, and the change of variables that perform such a reduction is also quasi-periodic with the same basic frequencies as Q.

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On the stability of a mixed functional equation deriving from additive, quadratic and cubic mappings

Cited by 11 publications

References 19 publications

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation

Almost additive-quadratic-cubic mappings in modular spaces

On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients

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