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Periodic boundary value problems for second order integro-differential equations of Volterra type. (English) Zbl 0569.45011

The existence of solutions of periodic boundary value problems for second order integro-differential equations is considered. When the function involved is assumed to be increasing relative to integral terms, the results become straightforward. On the other hand, when increasing nature is not assumed, the proofs break down since the existing comparison results demand it. This paper deals with this case and obtains deeper results.

MSC:

45J05 Integro-ordinary differential equations
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References:

[1] Aftabizadeh A. R., Proc. of Colloquia on Qualitative Theory of Differential Equations at Bolyai Institute (1984)
[2] Shouchuan Hu V. Lakshmikantham, Periodic boundary value problems for integro-differential equations of Volterra type · Zbl 0622.45007
[3] Laade G. S., Monotone Iterative Techniques for Nonlinear Differential Equations (1985)
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