New gaps between zeros of fourth-order differential equations via Opial inequalities
1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
2 Department of Mathematics, Texas A and M University-Kingsville, Kingsville, Texas, 78363, USA
3 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
Journal of Inequalities and Applications 2012, 2012:182 doi:10.1186/1029-242X-2012-182Published: 30 August 2012
In this paper, for a fourth-order differential equation, we will establish some lower bounds for the distance between zeros of a nontrivial solution and also lower bounds for the distance between zeros of a solution and/or its derivatives. We also give some new results related to some boundary value problems in the theory of bending of beams. The main results will be proved by making use of some generalizations of Opial and Wirtinger-type inequalities. Some examples are considered to illustrate the main results.
MSC: 34K11, 34C10.