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Lyapunov type integral inequalities for certain differential equations. (English) Zbl 0879.34013

The author establishes Lyapunov type integral inequalities related to the zeros of solutions of certain second-order differential equations as: \[ \bigl(r(t) |y' |^{\alpha -1} y'\bigr)'+ p(t)y'+ q(t)y+ f(t,y)=0, \]
\[ \bigl(r(t) |y|^\beta |y' |^{\gamma-2} y' \bigr)' +p(t)y' +q(t)y+ f(t,y)=0, \] by using elementary analysis. He also gives some applications to study the asymptotic behaviour of solutions of these differential equations.
Reviewer: S.Nocilla (Torino)

MSC:

34A34 Nonlinear ordinary differential equations and systems
26D10 Inequalities involving derivatives and differential and integral operators
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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