Results 261 to 270 of about 6,725,901 (296)

Nonoscillation of half‐linear dynamic equations on time scales

Mathematical Methods in the Applied Sciences, 2021
The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide the description of ...
P. Hasil, J. Kiselák, M. Pospíšil, M. Veselý   +3 more
semanticscholar   +3 more sources

On Oscillatory Behavior of Third Order Half-Linear Delay Differential Equations

Mathematica Slovaca, 2023
The authors examine the oscillatory behavior of solutions to a class of third order half-linear delay differential equations. The results are obtained by a comparison with first-order linear delay differential equations whose oscillatory characters are ...
S. Grace, J. Graef, E. Tunç
semanticscholar   +1 more source

Half‐Linear Eigenvalue Problems

Mathematische Nachrichten, 1997
AbstractWe consider the eigenvalue problem magnified image for t ϵ [0, b], where an = |a|n sgna, a ϵ ℝ, λ ϵ ℝ, the constants μ, v are real such that 0 ≤ μ < n and derive asymptotic estimates for solutions of the differential equation in the definite case q(t)> 0 which corresponds to the well‐known WKB‐approximation in the linear case n = 1, μ = 0.
Eberhard, Walter, Elbert, Árpad
openaire   +1 more source

Non‐oscillation of linear and half‐linear differential equations with unbounded coefficients

Mathematical methods in the applied sciences, 2020
We deal with Euler‐type half‐linear second‐order differential equations, and our intention is to derive conditions in order their non‐trivial solutions are non‐oscillatory. This paper connects to the article P. Hasil, J. Šišoláková, M.
J. Šišoláková
semanticscholar   +1 more source

Riccati technique and oscillation constant for modified Euler type half-linear equations

, 2020
Applying the modified half-linear Prufer angle, we study oscillation properties of certain half-linear differential equations. We show that the considered equations are conditionally oscillatory in a very general case.
M. Veselý, P. Hasil
semanticscholar   +1 more source

Conditionally oscillatory half-linear differential equations

Acta Mathematica Hungarica, 2008
The authors assume that a nonoscillatory solution to the half-linear equation \[ (r(t)\Phi(x'))+c(t)\Phi(x)=0,\;\Phi(x)=| x| ^{p-2}x,\;p>1, \] is known. Then they are able to construct a function \(d\) such that the (perturbed) equation \[ (r(t)\Phi(x'))+(c(t)+\lambda d(t))\Phi(x)=0 \] is conditionally oscillatory.
Došlý, O., Ünal, M.
openaire   +2 more sources

Nonoscillation in half-linear differential equations

Publicationes Mathematicae Debrecen, 1996
Necessary conditions are given for the nonoscillation of the solutions of the equation \[ [r(t)|u'(t)|^{p-2}u'(t)]'+c(t)|u(t)|^{p-2}u(t)=0, \] where \(p>1\) is a constant, and \(r(t)>0\).
Li, Horng-Jaan, Yeh, Cheh-Chih
openaire   +1 more source

Perturbations of the Half-Linear Euler Differential Equation

Results in Mathematics, 2000
The authors investigate oscillation/nonoscillation properties of the perturbed half-linear Euler differential equation \[ (x'{}^{n*})'+\frac{\gamma_0}{t^{n+1}}[n+2(n+1)\delta(t)]x^{n*}=0, \tag{*} \] where the function \(\delta(t)\) is piecewise continuous on \((t_0,\infty)\), \(t_0\geq 0\), \(n>0\) is a fixed real number and \(u^{n*}=|u|^n \text{sgn} u\
Elbert, Á., Schneider, A.
openaire   +2 more sources

Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments

Mathematica Slovaca, 2020
Neutral differential equations are one of the most important extensions of classical ordinary differential equations and aim to give a better explanation for modeling phenomena where ordinary differential equations are insufficient.
Simona Fisnarová, R. Mařík
semanticscholar   +1 more source