### Solving of Volterra's linear integral equations

K. Orlov, M. Stojanović (1974)

Matematički Vesnik

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K. Orlov, M. Stojanović (1974)

Matematički Vesnik

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R. Smarzewski (1976)

Applicationes Mathematicae

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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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Falaleev, M.V., Sidorov, N.A., Sidorov, D.N. (2005)

Lobachevskii Journal of Mathematics

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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.

Mydlarczyk, W. (2001)

Journal of Inequalities and Applications [electronic only]

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W. Mydlarczyk (1991)

Annales Polonici Mathematici

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W. Okrasinski (1993)

Extracta Mathematicae

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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, δ_{0}] → 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...

Piotr Ossowski, Janusz Zieliński (2010)

Colloquium Mathematicae

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We describe the ring of constants of a specific four variable Lotka-Volterra derivation. We investigate the existence of polynomial constants in the other cases of Lotka-Volterra derivations, also in n variables.