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

Título inglés	New conditions for the existence of non trivial solutions to some Volterra equations.
Título español	Nuevas condiciones para la existencia de soluciones no triviales de algunas ecuaciones de Volterra.
Autor/es	Okrasinski, W.
Organización	Inst. Math. Wroclaw Univ., Wroclaw, Polonia
Revista	0213-8743
Publicación	1990, 5 (1): 7-8, 5 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We consider the following Volterra equation: (1)       u(x) = ∫0x 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 solution u = 0. Some necessary and sufficient conditions for the existence of nontrivial solutions to (1) with k(x) = xα - 1 (α>0) are given in [1], [2] and [4]. In [3] and [5] conditions for more general kernels are presented. But those results do not give answers about nontrivial solutions in the case of kernels which are very smooth near the origin. Now we are able to show a necessary condition.
Clasificación UNESCO	120605
Palabras clave español	Ecuaciones de Volterra ; Soluciones ; Teorema de existencia
Código Z-Math	Zbl pre05143469
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