A family of singular ordinary differential equations of third order with an integral boundary condition

2017/04/03 by Mahdi Boukrouche, Boukrouche, Mahdi, Domingo A. Tarzia +1
Mathematics · #34A05 #34B10 #34B16 #35C15 #35K05 #35K20 #45D05 #45E10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:34A05 #msc:34B10 #msc:34B16 #msc:35C15 #msc:35K05 #msc:35K20 #msc:45D05 #msc:45E10

paper · pdf · doi:10.48550/arxiv.1704.00746

12 pages

arxiv created 2017/04/03 · arxiv updated 2017/04/05

Abstract

We establish in this paper the equivalence between a Volterra integral equation of second kind and a singular ordinary differential equation of third order with two initial conditions and an integral boundary condition, with a real parameter. This equivalence allow us to obtain the solution to some problems for nonclassical heat equation, the continuous dependence of the solution with respect to the parameter and the corresponding explicit solution to the considered problem.

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