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On the Global Solvability of the Cauchy Problem for Singular Functional Differential Equations

  • I. Kiguradze and Z. Sokhadze

Abstract

Sufficient conditions are found for the global solvability of the weighted Cauchy problem

where 𝑓 : 𝐢([π‘Ž, 𝑏]; 𝑅𝑛) β†’ πΏπ‘™π‘œπ‘(]π‘Ž, 𝑏]; 𝑅𝑛) is a singular Volterra operator, 𝑐0 ∈ 𝑅𝑛, 𝑕 : [π‘Ž, 𝑏] β†’ [0, +∞[ is a function continuous and positive on ]π‘Ž, 𝑏], and βˆ₯ Β· βˆ₯ is the norm in 𝑅𝑛.

Received: 1995-05-21
Published Online: 2010-03-03
Published in Print: 1997-August

Β© 1997 Plenum Publishing Corporation

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