Positive solutions of integro-differential inequalities. (English) Zbl 0906.26011
In the present paper, the authors have studied the nonexistence of positive solutions of the following integrodifferential inequalities
\[
(-1)^{n+ 1}y^{(n)}(t)+ \int^t_0 f(t- s,y(s))ds\leq 0
\]
on \([0,\infty)\) \((n = 1,2,4)\) assuming that the inequalities
\[
-\lambda^n+ \int^\infty_0 e^{\lambda^s} K(s)ds> 0,\quad\text{for all }\lambda>0\quad (n= 1,2,4)
\]
hold, where \(f\) and \(K\) satisfy certain suitable conditions.
Reviewer: B.G.Pachpatte (Aurangabad)
MSC:
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 45J05 | Integro-ordinary differential equations |
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