Displaying similar documents to “Remarks on a nonlinear Volterra equation”

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...