New gaps between zeros of fourth-order differential equations via Opial inequalities
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In this paper, for a fourth-order differential equation, the authors established lower bounds for the distance between zeros of a nontrivial solution and their derivatives, and for the boundary value problems in the theory of bending of beams.Abstract:
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; 34C10read more
Citations
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Discrete, Continuous, Delta, Nabla, and Diamond-Alpha Opial Inequalities
TL;DR: In this article, the authors proved diamond-alpha dynamic inequalities of Opial type with one and two weight functions on time scales, which contain as special cases improvements of results given in the literature, and these improvements are new even in the important discrete case.
Journal ArticleDOI
A General Dynamic Inequality of Opial Type
TL;DR: In this paper, the authors present a new general dynamic inequality of Opial type, which is new even in both the continuous and discrete cases and is proved by making use of a recently introduced new technique for Opial dynamic inequalities, the time scales integration by parts formula.
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Some generalizations of integral inequalities similar to Hardy’s inequality
S Bendaoud,Abdelkader Senouci +1 more
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Distribution of zeros of solutions of self-adjoint fourth order differential equations
Samir H. Saker,Donal O'Regan +1 more
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.
References
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Sharp Opial-Type Inequalities Involving Higher Order Derivatives of Two Functions
Ravi P. Agarwal,Peter Y. H. Pang +1 more
TL;DR: In this article, a very general Opial-type inequalities involving higher-order derivatives of two functions are presented, and extended and improved versions of several recent results are derived from these inequalities.
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Necessary conditions and sufficient conditions for disfocality and disconjugacy of a differential equation
TL;DR: In this article, a necessary and sufficient criterion for disconjugacy of the (k, n)-disconjoint equation y{n] + p(x)y = 0 is defined.
Liapunov-type integral inequalities for certain higher-order differential equations.
TL;DR: In this article, Liapunov-type integral inequalities for nonlinear, nonhomogeneous differential equations of higher order were obtained without any restriction on the zeros of their higher-order derivatives of the solutions by using elementary analysis.