Some properties of a non-linear integral Volterra equation with deviated argument
Bogdan Rzepecki (1976)
Annales Polonici Mathematici
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Bogdan Rzepecki (1976)
Annales Polonici Mathematici
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R. Smarzewski (1976)
Applicationes Mathematicae
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K. Orlov, M. Stojanović (1974)
Matematički Vesnik
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G. Karakostas (1987)
Colloquium Mathematicae
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Tvrdý, Milan (1997)
Memoirs on Differential Equations and Mathematical Physics
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Wojciech Mydlarczyk (1996)
Annales Polonici Mathematici
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We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.
H. Oka (1996)
Semigroup forum
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Yuri Lyubich, Dashdondog Tsedenbayar (2010)
Studia Mathematica
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The spectral problem (s²I - ϕ(V)*ϕ(V))f = 0 for an arbitrary complex polynomial ϕ of the classical Volterra operator V in L₂(0,1) is considered. An equivalent boundary value problem for a differential equation of order 2n, n = deg(ϕ), is constructed. In the case ϕ(z) = 1 + az the singular numbers are explicitly described in terms of roots of a transcendental equation, their localization and asymptotic behavior is investigated, and an explicit formula for the ||I + aV||₂ is given. For...
Mydlarczyk, W. (2001)
Journal of Inequalities and Applications [electronic only]
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M. Niedziela (2008)
Applicationes Mathematicae
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The behaviour near the origin of nontrivial solutions to integral Volterra equations with a power nonlinearity is studied. Estimates of nontrivial solutions are given and some numerical examples are considered.
W. Okrasinski (1990)
Extracta Mathematicae
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We consider the following Volterra equation: (1) u(x) = ∫0 x k(x-s) g(u(s)) ds, where, k: [0, δ0] → R is an increasing absolutely continuous function such that k(0) = 0 g: [0,+ ∞) → [0,+ ∞) is an increasing absolutely continuous function such that g(0) = 0 and g(u)/u → ∞ as u → 0+ (see [3]). Let us note that (1) has always...
W. Okrasinski (1993)
Extracta Mathematicae
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W. Mydlarczyk (1991)
Annales Polonici Mathematici
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