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Displaying similar documents to “Nontrivial solutions to nonlinear Volterra equations”

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...

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.

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.

Uniqueness of solutions to an Abel type nonlinear integral equation on the half line

Wojciech Mydlarczyk (2012)

Open Mathematics

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We consider a convolution-type integral equation u = k ⋆ g(u) on the half line (−∞; a), a ∈ ℝ, with kernel k(x) = x α−1, 0 < α, and function g(u), continuous and nondecreasing, such that g(0) = 0 and 0 < g(u) for 0 < u. We concentrate on the uniqueness problem for this equation, and we prove that if α ∈ (1, 4), then for any two nontrivial solutions u 1, u 2 there exists a constant c ∈ ℝ such that u 2(x) = u 1(x +c), −∞ < x. The results are obtained by applying Hilbert projective...