2021
DOI: 10.3390/axioms10030192
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Oscillation and Asymptotic Properties of Differential Equations of Third-Order

Abstract: The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ι−τ)′)′]β)′+∫cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ι≥ι0 and w(ι):=x(ι)+p(ι)x(ι−τ). New oscillation results are established by using the generalized Riccati technique under the assumption of ∫ι0ιa−1/β(s)ds<∫ι0ι1b(s)ds=∞asι→∞. Our new results complement the related contribution… Show more

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Cited by 4 publications
(2 citation statements)
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“…The authors examined and celebrated conformable and non-conformable derivative in the published articles [19] and [20]. Both fractional integral operators have a lot of meaningful and useful applications, see the references [21][22][23][24][25][26][27][28][29]. Definition 3.…”
Section: Preliminariesmentioning
confidence: 99%
“…The authors examined and celebrated conformable and non-conformable derivative in the published articles [19] and [20]. Both fractional integral operators have a lot of meaningful and useful applications, see the references [21][22][23][24][25][26][27][28][29]. Definition 3.…”
Section: Preliminariesmentioning
confidence: 99%
“…Questions that arise in economics, physics, biology, etc., lead to mathematical models, which are often formulated in the form of functional equations of various types, in particular, differential, integro-differential and difference equations (see, for example, [1][2][3][4][5][6][7]). One of the fundamental problems in approaches to finding solutions of such equations is the reconstruction of functions of one or several variables, as well as problems that arise in the development and implementation of effective methods and algorithms for representing and approximating the functions of one or several variables.…”
Section: Introductionmentioning
confidence: 99%