Results 241 to 250 of about 82,878 (275)

Parametric Centers for Trigonometric Abel Equations

Journal of Dynamics and Differential Equations, 2008
his article is devoted to one-dimensional perturbative theory on R × S1. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques.
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A functional equation of abel revisited

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1994
The equation \(g(x) + g(y) = h(xf(y) + yf(x))\) \((f,g,h\) unknown) was solved by \textit{N. H. Abel} [J. Reine Angew. Math. 21, 386-394 (1827)] under differentiability suppositions. It also belonged to those functional equations which D. Hilbert in 1900, in the second part of the fifth of his famous unsolved problems, proposed for solution under ...
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Functions Which Satisfy Abel’s Differential Equation

SIAM Journal on Applied Mathematics, 1967
(4) 4)13 + (P23 + 033 30)10203 = 1. The addition formulae and other properties have been given in recent times by Silberstein [1], Oniga [2] and Bruwier [3], [4], while Mikusinski [5], [6] and Poli [7], [8] have studied the corresponding third order circular functions. Earlier workers in this field were Appell [9], Glaisher [10] and Villarceau [11]. It
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Regularization of an Abel equation

Integral Equations and Operator Theory, 1997
A class of Abel equations in the space \(C_0[0,1]\) of continuous functions with compact supports are replaced with their finite difference approximations on a uniform grid and then regularized by the standard Tikhonov method. Estimates for regularized and discretized finite-dimensional solutions of the initial value problem are presented in the case ...
Wang, Ping, Zheng, Kewang
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Group iteration for Abel’s functional equation

Nonlinear Analysis: Hybrid Systems, 2007
Some group-theoretic iteration technique is developed for an investigation of the generalized Abel functional equation \[ \alpha(f(x))= g(\alpha(x)). \] The technique is based on a change of a variable in intervals between adjacent fixed points of the given function \(f\).
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Abel Equations and Generalizations

2009
In this chapter, Abel’s equation, exponential iteration, associative and commutative equations, trigonometric equations, and systems of equations are treated. Generalizations and connections to information measures are treated. Hilbert, in his famous address to the International Congress of Mathematicians held in Paris in 1900 [372], posed many ...
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Abel Integral Equations

2023
Sudeshna Banerjea, Birendra Nath Mandal
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Shock Waves and Abel's Differential Equation

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1964
AbstractIt ist shown that the ordinary non‐linear second order differential equation of the phenomenological theory of the one‐dimensional steady shock wave in heat conducting viscous gases can be transformed into the Abelian differential equation of the second class.
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Poisson’s Equation for Abel-Ergodic Theorems

Complex Analysis and Operator Theory
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A nonlinear Abel integral equation

2006
For the general nonlinear Abel integral equation $$\frac{1}{{\Gamma (\alpha )}}\int\limits_0^x {(x - t)^{\alpha - 1} K(x,t,u(t))dt = f(x),{\text{ 0}} \leqslant x \leqslant 1,0 < \alpha < 1,}$$ some theorems on existence and uniqueness of solutions in L P , 1≤p≤∞, and in C[0, 1] are established.
Dang Dinh Ang, Rudolf Gorenflo
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