EUDML

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 trivial...

About the interface of some nonlinear diffusion problems.

J. Goncerzewicz; W. Okrasinski — 1994

Extracta Mathematicae

Boyd index and nonlinear Volterra equations.

Jesús M. Fernández Castillo; W. Okrasinski — 1991

Extracta Mathematicae

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.

On the percolation of water from a cylindrical reservoir into the surrounding soil

J. Goncerzewicz; H. Marcinkowska; W. Okrasiński; K. Tabisz — 1978

Applicationes Mathematicae

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On a generalization of the Osgood condition.

On a nonlinear ordinary differential equation

On the existence and uniqueness of non-negative solutions of a certain non-linear convolution equation

Some remarks about the infiltration of water from a cylindrical reservoir

On a nonlinear convolution equation occurring in the theory of water percolation

On a certain nonlinear equation

Note on the asymptotic behaviour of the interface of some nonlinear diffusion problems.

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

Note on some integral Volterra equations.

Nonexistence of nontrivial solutions to some nonlinear Volterra equations.

Note on nontrivial solutions to nonlinear Volterra equations.

Nontrivial solutions to nonlinear Volterra equations

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

About the interface of some nonlinear diffusion problems.

Boyd index and nonlinear Volterra equations.

On the percolation of water from a cylindrical reservoir into the surrounding soil