著者

Hideshi Yamane

出版者

Division of Functional Equations, The Mathematical Society of Japan

雑誌

Funkcialaj Ekvacioj (ISSN:05328721)

巻号頁・発行日

vol.66, no.3, pp.159-193, 2023-12-15 (Released:2023-12-13)

参考文献数

19

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We solve the analytic Cauchy problem for the generalized two-component Camassa-Holm system introduced by R. M. Chen and Y. Liu. We show the existence of a unique local/global-in-time analytic solution under certain conditions. This is the first result about global analyticity for a Camassa-Holm-like system. The method of proof is basically that developed by Barostichi, Himonas and Petronilho. The main differences between their proof and ours are twofold: (i) the system of Chen and Liu is not symmetric in the two unknowns and our estimates are not trivial generalization of those in their articles, (ii) we have simplified their argument by using fewer function spaces and the main result is stated in a simple and natural way.

著者

Hideshi Yamane

出版者

Division of Functional Equations, The Mathematical Society of Japan

雑誌

Funkcialaj Ekvacioj (ISSN:05328721)

巻号頁・発行日

vol.62, no.2, pp.227-253, 2019 (Released:2019-08-26)

参考文献数

20

被引用文献数

1 3

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We investigate the long-time asymptotics for the focusing integrable discrete nonlinear Schrödinger equation. Under generic assumptions on the initial value, the solution is asymptotically a sum of 1-solitons. We find different phase shift formulas in different regions. Along rays away from solitons, the behavior of the solution is decaying oscillation. This is one way of stating the soliton resolution conjecture. The proof is based on the nonlinear steepest descent method.

著者

David Sauzin

出版者

Division of Functional Equations, The Mathematical Society of Japan

雑誌

Funkcialaj Ekvacioj (ISSN:05328721)

巻号頁・発行日

vol.56, no.3, pp.397-413, 2013 (Released:2013-12-19)

参考文献数

11

被引用文献数

3 7

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This article introduces, for any closed discrete subset Ω of C, the definition of Ω-continuability, a particular case of Écalle's resurgence: Ω-continuable functions are required to be holomorphic near 0 and to admit analytic continuation along any path which avoids Ω. We give a rigorous and self-contained treatment of the stability under convolution of this space of functions, showing that a necessary and sufficient condition is the stability of Ω under addition.

著者

Anello Giovanni

出版者

日本数学会函数方程式論分科会

雑誌

Funkcialaj Ekvacioj (ISSN:05328721)

巻号頁・発行日

vol.59, no.1, pp.113-122, 2016

被引用文献数

3

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Let Ω be a bounded domain in RN with smooth boundary. Let f: [0, + ∞[ → [0,+∞[, with f(0) = 0, be a continuous function such that, for some a > 0, the function ξ∈]0, +∞[ → ξ−2 · ∫0ξ f(t)dt is non increasing in ]0,a[. Finally, let α: <span style="text-decoration: overline">Ω</span> → [0,+∞[ be a continuous function with α(x) > 0, for all x ∈ Ω. We establish a necessary and sufficient condition for the existence of solutions to the following problem −Δu = λα(x)f(u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, where λ is a positive parameter. Our result extends to higher dimension a similar characterization very recently established by Ricceri in the one dimensional case.

著者

Hassane Bouzahir Honglian You Rong Yuan

出版者

日本数学会函数方程式論分科会

雑誌

Funkcialaj Ekvacioj (ISSN:05328721)

巻号頁・発行日

vol.54, no.1, pp.139-156, 2011 (Released:2011-04-21)

参考文献数

38

被引用文献数

6 8

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This paper deals with a class of partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined, and employing the integrated semigroups and dissipative dynamics theory, we present some appropriate conditions to guarantee existence of a global attractor.

著者

Mikio Murata

出版者

日本数学会函数方程式論分科会

雑誌

Funkcialaj Ekvacioj (ISSN:05328721)

巻号頁・発行日

vol.47, no.2, pp.291-305, 2004 (Released:2004-09-15)

参考文献数

8

被引用文献数

5 13

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We present a new expression for the elliptic-difference Painlevé equation. As in our construction all parameters in their equations appear in a symmetric way, the permutation symmetry of the equations is immediately apparent. We present expressions for other discrete Painlevé equations, obtained in a similar way.