Linearized oscillation theory for a nonlinear equation with a distributed delay

Authors:
Leonid Berezansky;Elena Braverman
Affiliations:
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

We obtain linearized oscillation theorems for the equation with distributed delays (1)x@?(t)+@?k=1mr"k(t)@!"-"~^tf"k(x(s))d"sR"k(t,s)=0. The results are applied to logistic, Lasota-Wazewska and Nicholson's blowflies equations with a distributed delay. In addition, the ''Mean Value Theorem'' is proved which claims that a solution of (1) also satisfies the linear equation with a variable concentrated delay x@?(t)+(@?k=1mr"k(t)f"k^'(@x"k(t)))x(g(t))=0.