Geodesic
Oscillation for equations with positive and negative coefficients and distributed delay. II: Applications
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study a scalar delay differential equation with a bounded distributed delay, $$ \dot{x}(t)+ \int_{h(t)}^t x(s)\,d_s R(t,s) - \int_{g(t)}^t x(s)\,d_s T(t,s)=0, $$ where $$ R(t,h(t))=T(t,g(t))=0, \quad R(t,s) \geq T(t,s). $$ We establish a connection between non-oscillation of this differential equation and the corresponding differential inequalities, and between positiveness of the fundamental function and the existence of a nonnegative solution for a nonlinear integral inequality that constructed explicitly. We also present comparison theorems, and explicit non-oscillation and oscillation results. In a separate publication (part II), we will consider applications of this theory to differential equations with several concentrated delays, integrodifferential, and mixed equations.
Classification : 34K11, 34K15
Keywords: oscillation, non-oscillation, distributed delay, comparison theorems 
@article{EJDE_2003__2003__a68,
     author = {Berezansky, Leonid and Braverman, Elena},
     title = {Oscillation for equations with positive and negative coefficients and distributed delay. {II:} {Applications}},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a68/}
}
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Berezansky, Leonid; Braverman, Elena. Oscillation for equations with positive and negative coefficients and distributed delay. II: Applications. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a68/