Distribution of zeros and disconjugacy of fourth order differential equations. Issue 1 (23rd September 2015)

• Record Type: Journal Article
• Authors: Saker, S. H.; Kubiaczyk, I.
• Is Part Of: Mathematische Nachrichten. Volume 289:Issue 1(2016)
• Page Start: 97
• Page End: 115
• Publication Date: 2015-09-23
• Subjects: Fourth‐order differential equations -- bending of beams -- Opial and Wirtinger inequalities -- 34C10 -- 34K11; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201200114
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : In this paper, we study the gaps between zeros of nontrivial solutions of fourth order differential equations subject to some boundary conditions, and establish some sufficient conditions for (2, 2)‐disconjugacy. The results, which cover some boundary value problems in bending of beams, will be proved by making use of a generalization of Hardy's inequality and some Opial and Wirtinger type inequalities. Some examples are considered to illustrate the main results.