Results 251 to 260 of about 83,200 (280)

Generalized Abel Equation

2003
Generalized Abel equations have the form $$ \phi \left( {F\left( x \right)} \right) = g\left( {x,\phi \left( x \right)} \right) $$ (3.0.1) where F : M → M is a given mapping, g(x, y) is a given function of x ∈ M, y∈ℝ and φ(x) is a solution. The Abel, Schroder and cohomological equations are particular cases of (3.0.1).
Genrich Belitskii, Vadim Tkachenko
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Abel Integral Equations

1990
Even though they have a rather specialized structure, Abel equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. After an initial survey of Abel integral equations, this chapter focuses on the numerical solution of these equations when the ...
R. S. Anderssen, F. R. Hoog
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Abel’s Equations

2012
In this chapter we study the structure of the set of curves M associated with real polynomials of degree n by means of the Chebyshev correspondence.
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Regularization of the Abel Integral Equation with Perturbation

Computational Mathematics and Mathematical Physics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
G V Khromova
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Qualitative Analysis of a Differential Equation of Abel

The American Mathematical Monthly, 2008
(2008). Qualitative Analysis of a Differential Equation of Abel. The American Mathematical Monthly: Vol. 115, No. 2, pp. 147-149.
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Abel’s Integral Equation

1995
The following Volterra integral equation of the first kind is due to Abel (1823): $$g(x) = \int\limits_a^x {\frac{{f(y)}} {{\sqrt {x - y} }}dy\;for\;x \geqslant a}$$ (6.1.1) . Since the denominator \(\sqrt {x - y} \) has a zero at y=x, the integral in (1) is to be understood in the improper sense (cf.
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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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An Existence Theorem for Abel Integral Equations

SIAM Journal on Mathematical Analysis, 1974
An existence and smoothness theorem is given for the Abel integral equation $\int _0^s K(s,t)f(t)(s^p - t^p )^{ - \alpha } dt = g(s)$, $0 0$ and $0 < \alpha < 1$. Particular attention is given to the behavior of $g(s)$ and $f(s)$ about $s = 0$.
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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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On polygonal approximation in solving Abel’s equation

Journal of Mathematical Sciences, 1995
On the interval \([a, b]\) of the real line we consider Abel's integral equation \[ \int^x_a {\varphi(t) dt\over (x- t)^\alpha}= g(x),\quad 0< \alpha< 1,\tag{1} \] where \(g(x)\) is a given real-valued function of Hölder class: \[ |g(x)- g(t)|\leq A|x- t|^\mu,\quad \mu> 1- \alpha;\quad x, t\in [a,b].
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