Displaying similar documents to “On a Staffans type inequality for vector Volterra integro-differential equations”

Boyd index and nonlinear Volterra equations.

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.

New conditions for the existence of non trivial solutions to some Volterra 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...

The existence of solutions to a Volterra integral equation

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.