Geodesic
Lyapunov type inequalities for a second order differential equation with a damping term
S. H. Saker1
1 Department of Mathematics Skills, PYD King Saud University Riyadh 11451, Saudi Arabia and Department of Mathematics Mansoura University Mansoura 35516, Egypt
Annales Polonici Mathematici, Tome 103 (2012) no. 1, pp. 37-57

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap103-1-4
Keywords: second order differential equation damping term establish inequalities lyapunov type these inequalities implicit lower bounds distance between zeros nontrivial solution lower bounds spacing between zeros solution its derivative obtain lower bound first eigenvalue boundary value problem main results proved applying lder inequality generalizations opial wirtinger type inequalities results yield conditions disfocality disconjugacy example considered illustrate main results

S. H. Saker 1

1 Department of Mathematics Skills, PYD King Saud University Riyadh 11451, Saudi Arabia and Department of Mathematics Mansoura University Mansoura 35516, Egypt 
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S. H. Saker. Lyapunov type inequalities for a
 second order differential equation with a damping term. Annales Polonici Mathematici, Tome 103 (2012) no. 1, pp. 37-57. doi: 10.4064/ap103-1-4

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