Lyapunov type inequalities for a second order differential equation with a damping term

S. H. Saker. "Lyapunov type inequalities for a second order differential equation with a damping term." Annales Polonici Mathematici 103.1 (2012): 37-57. <http://eudml.org/doc/281017>.

@article{S2012,
abstract = {For a second order differential equation with a damping term, we establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivative. We also obtain a lower bound for the first eigenvalue of a boundary value problem. The main results are proved by applying the Hölder inequality and some generalizations of Opial and Wirtinger type inequalities. The results yield conditions for disfocality and disconjugacy. An example is considered to illustrate the main results.},
author = {S. H. Saker},
journal = {Annales Polonici Mathematici},
keywords = {Lyapunov inequality; second-order differential equation; damping term; disfocality; disconjugacy; first eigenvalue},
language = {eng},
number = {1},
pages = {37-57},
title = {Lyapunov type inequalities for a second order differential equation with a damping term},
url = {http://eudml.org/doc/281017},
volume = {103},
year = {2012},
}

TY - JOUR
AU - S. H. Saker
TI - Lyapunov type inequalities for a second order differential equation with a damping term
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 1
SP - 37
EP - 57
AB - For a second order differential equation with a damping term, we establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivative. We also obtain a lower bound for the first eigenvalue of a boundary value problem. The main results are proved by applying the Hölder inequality and some generalizations of Opial and Wirtinger type inequalities. The results yield conditions for disfocality and disconjugacy. An example is considered to illustrate the main results.
LA - eng
KW - Lyapunov inequality; second-order differential equation; damping term; disfocality; disconjugacy; first eigenvalue
UR - http://eudml.org/doc/281017
ER -