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Properties of Kneser’s solution for half-linear third order neutral differential equations

Acta Mathematica Hungarica, 2017
The authors consider the third-order neutral differential equation of advanced type \[ (a(t)(b(t)(z'(t))^\alpha)')'+q(t)y^\alpha(t)=0, \] where \(\alpha\) is a ratio of odd positive integers, \(z(t)=y(t)+p(t)y(\sigma(t))\), \(\sigma(t)\geq t\), \(a,b,\sigma,q\) are continuous and positive functions, and some other hypotheses are assumed.
Baculikova, B., Rani, B., Selvarangam, S., Thandapani, E.   +3 more
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Properties of Kneser solutions for third-order differential equations

Applied Mathematics and Computation, 2017
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Džurina, J., Baculíková, B.
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Nonoscillating Kneser Solutions of the Emden–Fawler Equation

Differential Equations, 2000
Here, the Emden-Fowler equation \[ u^{(n)}=(-1)^np(t)|u|^\lambda \text{sgn}u, \quad ...
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Blow-Up Kneser Solutions of Nonlinear Higher-Order Differential Equations

Differential Equations, 2001
A solution \( u : (0,\infty) \to \mathbb{R}\) to the differential equation \[ u^{(n)}= f(t,u,\dots, u^{(n-1)}),\qquad n \geq 2, \tag{*} \] where \( f : (0, \infty)\times \mathbb{R}^ n \to \mathbb{R}\) is continuous in \(x_1,\dots,x_n\) for almost all \(t \in (0,\infty)\) and measurable in \(t\) for all \((x_1,\dots, x_n) \in \mathbb{R}^n,\) \(f(t, 0 ...
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Kneser's theorem for weak solutions of the Darboux problem in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 1993
Let \(E\) be a weakly sequentially complete Banach space, \(B=\{z\in E;\| z\|\leq b\}\), \(D=[0,a_ 1]\times[0,a_ 2]\) and \(f:D\times B\to E\), a weakly-weakly continuous function such that \(\| f(x,y,z)\|\leq M\forall (x,y,z)\in D\times B\).
Bugajewski, Dariusz, Szufla, Staniśław
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Asymptotic properties of Kneser solutions to nonlinear second order ODEs with regularly varying coefficients

Applied Mathematics and Computation, 2016
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Burkotová, Jana, Hubner, Michael, Rachunková, Irena, Weinmüller, Ewa B.   +3 more
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ASYMPTOTIC BEHAVIOR OF KNESER’S SOLUTION FOR SEMI-CANONICAL THIRD-ORDER HALF-LINEAR ADVANCED NEUTRAL DIFFERENTIAL EQUATIONS

Functional Differential Equations, 2022
In this paper, we study the properties of positive solutions of the thirdorder neutral differential equations with advanced argument of the form (p(t)(q(t)(z′(t))α)′)′ + f(t)xα(τ (t)) = 0, where z(t) = x(t) + g(t)(x(σ(t))). First we obtain conditions for the existence of Kneser type solutions and then provide lower and upper estimate that yield the ...
K. SARANYA, V. PIRAMANANTHAM, E. THANDAPANI, E. TUNC   +3 more
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Weight functions on the Kneser graph and the solution of an intersection problem of Sali

Combinatorica, 1993
Let \(X,Y\) be disjoint finite sets. The family \({\mathcal F}=\{(F,G)\} \subset 2^ X \times 2^ Y\) is \((s,t,u)\)-intersecting if every pair \((F,G)\), \((F',G') \in {\mathcal F}\) satisfies \(| F \cap F' | \geq s\), \(| G \cap G' | \geq t\), and \(| F \cap F' |+| G \cap G' | \geq u\). The paper generalizes a result of Sali and gives exact upper bound
Frankl, Peter, Tokushige, Norihide
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Kneser's theorem for weak solutions of an mth-order ordinary differential equation in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 1999
The author deals with the Cauchy problem \[ x^{(n)}= f(t,x), \quad x(0)=0, \quad x'(0)= \eta_1,\ldots, x^{(n-1)}(0)=\eta_{n-1}, \tag{*} \] where the function \(f:J\times B \to E\) is bounded and weakly-weakly continuous, \(J= [0,a]\) and \(B\) is a unit ball in the sequentially weakly complete Banach space \(E\).
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Izobov’s Problem on Kneser Solutions of Singular Nonlinear Differential Equations of the Second and Third Order

Differential Equations, 2020
The differential equation \[ y^{(n)}(x)=p(x)|y(x)|^k \operatorname{sign} y(x), \ \ x\geq0, \ \ n\in N, \ \ n\geq2,\ \ k\in(0,1).\tag{1} \] where ...
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