On Some Inverse Problems of the Calculus of Variations for Second Order Differential Equations with Deviating Arguments and Partial Derivatives

2014 ◽  
pp. 253-270
Author(s):  
Galina Kurina
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Calculus Of Variations ◽  
Second Order ◽  
Deviating Arguments ◽  
Partial Derivatives ◽  
Second Order Differential Equations

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

Nonlinear Multipoint Boundary Value Problems for Second Order Differential Equations

2010 ◽  
Vol 53 (3) ◽  
pp. 475-490
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Arguments ◽  
Multipoint Boundary ◽  
Monotone Iterative ◽  
Second Order Differential Equations ◽  
Multipoint Boundary Value Problems

AbstractIn this paper we shall discuss nonlinear multipoint boundary value problems for second order differential equations when deviating arguments depend on the unknown solution. Sufficient conditions under which such problems have extremal and quasi-solutions are given. The problem of when a unique solution exists is also investigated. To obtain existence results, a monotone iterative technique is used. Two examples are added to verify theoretical results.

scholarly journals Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2552
Author(s):  
Blanka Baculikova
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Second Order ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
Second Order Differential Equations ◽  
Linear Differential ◽  
New Criteria ◽  
Mixed Argument

In this paper, we study oscillation and asymptotic properties for half-linear second order differential equations with mixed argument of the form r(t)(y′(t))α′=p(t)yα(τ(t)). Such differential equation may possesses two types of nonoscillatory solutions either from the class N0 (positive decreasing solutions) or N2 (positive increasing solutions). We establish new criteria for N0=∅ and N2=∅ provided that delayed and advanced parts of deviating argument are large enough. As a consequence of these results, we provide new oscillatory criteria. The presented results essentially improve existing ones even for a linear case of considered equations.

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