Opial's type inequalities on time scales and some applications

@article{S2012,
abstract = {We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential equations, give some new results for difference equations and yield conditions for disfocality for second order dynamic equations on time scales.},
author = {S. H. Saker},
journal = {Annales Polonici Mathematici},
keywords = {Opial's inequality; disfocality; generalized zero; Sturm-Liouville eigenvalue problem},
language = {eng},
number = {3},
pages = {243-260},
title = {Opial's type inequalities on time scales and some applications},
url = {http://eudml.org/doc/280416},
volume = {104},
year = {2012},
}

TY - JOUR
AU - S. H. Saker
TI - Opial's type inequalities on time scales and some applications
JO - Annales Polonici Mathematici
PY - 2012
VL - 104
IS - 3
SP - 243
EP - 260
AB - We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential equations, give some new results for difference equations and yield conditions for disfocality for second order dynamic equations on time scales.
LA - eng
KW - Opial's inequality; disfocality; generalized zero; Sturm-Liouville eigenvalue problem
UR - http://eudml.org/doc/280416
ER -