On a Staffans type inequality for vector Volterra integro-differential equations
G. Karakostas (1987)
Colloquium Mathematicae
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G. Karakostas (1987)
Colloquium Mathematicae
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W. Okrasinski (1993)
Extracta Mathematicae
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Jesús M. Fernández Castillo, W. Okrasinski (1991)
Extracta Mathematicae
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In mathematical models of some physical phenomena a new class of nonlinear Volterra equations appears ([5],[6]). The equations belonging to this class have u = 0 as a solution (trivial solution), but with respect to their physical meaning, nonnegative nontrivial solutions are of prime importance.
Mydlarczyk, W. (2001)
Journal of Inequalities and Applications [electronic only]
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Bogdan Rzepecki (1976)
Annales Polonici Mathematici
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K. Orlov, M. Stojanović (1974)
Matematički Vesnik
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R. Smarzewski (1976)
Applicationes Mathematicae
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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 (1989)
Extracta Mathematicae
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R. Jeltsch, Jennifer Dixon, S. McKee (1986)
Numerische Mathematik
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W. Mydlarczyk (1988)
Applicationes Mathematicae
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Tvrdý, Milan (1997)
Memoirs on Differential Equations and Mathematical Physics
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