Distribution of zeros of solutions of self-adjoint fourth order differential equations
01 Jan 2014-egyptian journal of basic and applied sciences (No longer published by Elsevier)-Vol. 1, Iss: 1, pp 49-59
TL;DR: In this article, lower bounds on the distance between zeros of a nontrivial solution and their derivatives were established for self-adjoint fourth-order differential equations, by making use of some generalizations of Hardy, Opial and Wirtinger type inequalities.
Abstract: In this paper, for self-adjoint fourth order differential equations, we establish some lower bounds on the distance between zeros of a nontrivial solution and also lower bounds on the distance between zeros of a solution and/or its derivatives. We also give new results related to boundary value problems which arise in the bending of rods. The main results will be proved by making use of some generalizations of Hardy, Opial and Wirtinger type inequalities.
References
More filters
Book•
01 Jan 1992
TL;DR: Zill's writing style has been highly praised by reviewers as easy-to-read, understandable and helpful to readers as discussed by the authors, and has been described as "easy to read, understandable, and helpful".
Abstract: Systems of Differential Equations Fourier Series and Boundary-Value Problems Numerical Analysis Complex Analysis. Zill's writing style has been highly praised by reviewers as easy-to-read, understandable and helpful to readers.
1,232 citations
Book•
08 Apr 2003
TL;DR: Hardy's Inequality and Related Topics Some Weighted Norm Inequalities The Hardy Steklov Operator Higher Order Hardy Inequality Fractional Order Hardy-Steklov Operators on the Cone of Monotone Functions as discussed by the authors.
Abstract: Hardy's Inequality and Related Topics Some Weighted Norm Inequalities The Hardy-Steklov Operator Higher Order Hardy Inequalities Fractional Order Hardy Inequalities Integral Operators on the Cone of Monotone Functions.
596 citations
Book•
17 Feb 2016
480 citations
01 Jan 2007
TL;DR: The Hardy inequality has a fascinating past and will have (hopefully) also a fascinating future as mentioned in this paper, and the authors present some important steps of the development of the classical Hardy inequality.
Abstract: The Hardy inequality has a fascinating past and will have (hopefully) also a fascinating future. Here, the authors present some important steps of the development of the classical Hardy inequality ...
425 citations