Showing papers on "Aizerman's conjecture published in 2004"
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TL;DR: In this paper, conditions for the positivity and boundedness of the Green functions of the higher-order linear nonautonomous ODE were derived, and the existence of positive solutions for a class of nonlinear equations was proved.
Abstract: We derive conditions for the positivity
and boundedness of the Green functions of the higher order linear nonautonomous ODE.
By virtue of these conditions, the existence of positive solutions
for a class of nonlinear equations is proved. In addition,
upper and lower estimates for the Green functions
are established. Moreover, it is shown that nonlinear equations, having separated nonautonomous linear parts,
satisfy the generalized Aizerman hypothesis on absolute stability, if they have the positive Green functions.
3 citations