Pachpatte, B. G. Lyapunov type integral inequalities for certain differential equations. (English) Zbl 0879.34013 Georgian Math. J. 4, No. 2, 138-148 (1997). 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) Cited in 41 Documents 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 Keywords:second-order differential equations; asymptotic behaviour of solutions PDFBibTeX XMLCite \textit{B. G. Pachpatte}, Georgian Math. J. 4, No. 2, 138--148 (1997; Zbl 0879.34013) Full Text: EuDML EMIS