Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations

Zdeněk Šmarda
2010 Advances in Difference Equations  
The existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem: g t y t ay t 1 f t, y t , t 0 K t, s, y t , y s ds , y 0 0, t ∈ 0, t 0 , where a > 0 is a constant and t 0 > 0. An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used. Ω 0k { t, Y 0 : 0 < t < t * , u 0k t, Y 0 < 0}, 2.30
doi:10.1155/2010/810453 fatcat:gotre6l77ja7bhqkdn4ba7znpm