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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Mydlarczyk, W. (2001)
Journal of Inequalities and Applications [electronic only]
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Jan Bochenek (1992)
Annales Polonici Mathematici
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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.
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...
H. Oka (1996)
Semigroup forum
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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 (1993)
Extracta Mathematicae
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G. Karakostas (1987)
Colloquium Mathematicae
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