Existence of nonoscillatory solutions of the third order quasilinear neutral differential equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 0999.34063
author: Vladimír Janík
author: Pavol Marušiak
publication date: 2002-02-27T00:00:00Z
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1675624
zbMATH Keywords: quasilinear neutral differential equation
zbMATH Keywords: nonoscillatory solution
zbMATH Keywords: existence
zbMATH Keywords: Schauder-Tikhonov fixed-point theorem
MaRDI profile type: Publication
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title: Existence of nonoscillatory solutions of the third order quasilinear neutral differential equations
published in: Fasciculi Mathematici
review text: The authors consider third-order quasilinear neutral differential equations of the form NEWLINE\[NEWLINE (r_2(t)(r_1(t)\varphi (L_0'x(t)))')'+f(t, x(g(t)))=0,\quad t\geq a\geq 0, NEWLINE\]NEWLINE with \(L_0x(t)=x(t)-p(t)x(h(t))\). First, they classify the nonoscillatory solutions in the set \(N^+=\{x\) is a nonoscillatory solution to the above equation: \(x(t)L_0x(t)>0\) for all large \(t\}\) into three types. Then, by using the Schauder-Tikhonov fixed-point theorem, they establish sufficient and necessary conditions for the existence of nonoscillatory solutions to the above equation for each type with specified asymptotic behavior as \(t\rightarrow \infty\).
reviewed by: Qiru Wang
description: scientific article; zbMATH DE number 1675624