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INICIO | 19 de mayo de 2024
  

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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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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