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

• Autorzy: S. H. Saker
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 34K10: Boundary value problems
• 34K11: Oscillation theory
• 34C10: Oscillation theory, zeros, disconjugacy and comparison theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 103
• Numer: 1
• Strony: 37-57

Daty

wydano

2012

Twórcy

autor

S. H. Saker

• Department of Mathematics Skills, PYD, King Saud University, Riyadh 11451, Saudi Arabia
• Department of Mathematics, Mansoura University, Mansoura 35516, Egypt

Identyfikatory

DOI

10.4064/ap103-1-4