Nonexistence of nontrivial solutions to some nonlinear Volterra equations.

W. Okrasinski

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Displaying similar documents to “Nonexistence of nontrivial solutions to some nonlinear Volterra equations.”

Nontrivial solutions to nonlinear Volterra equations

W. Okrasinski (1989)

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Boyd index and nonlinear Volterra equations.

Jesús M. Fernández Castillo, W. Okrasinski (1991)

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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.

Note on some integral Volterra equations.

W. Okrasinski (1993)

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A Volterra inequality with the power type nonlinear kernel.

Mydlarczyk, W. (2001)

Journal of Inequalities and Applications [electronic only]

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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...

Remarks on a nonlinear Volterra equation

W. Mydlarczyk (1991)

Annales Polonici Mathematici

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Nonlinear Volterra equations and physical applications. [Appendix: On an extension of Gripenberg's condition].

W. Okrasinski (1989)

Extracta Mathematicae

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On a Volterra integral equation with deviating arguments.

Balachandran, Krishnan (1990)

Journal of Applied Mathematics and Stochastic Analysis

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On a Staffans type inequality for vector Volterra integro-differential equations

G. Karakostas (1987)

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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...

Hysteresis in Urysohn-Volterra systems.

Darwish, Mohamed Abdalla (1999)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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On Volterra inequalities and their applications.

Ha̧cia, Lechosław (2004)

International Journal of Mathematics and Mathematical Sciences

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