Results 21 to 30 of about 58,243 (254)
Conjugacy and principal solution of generalized half-linear second order differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2012 We study the generalized half-linear second order differential equation and the associated Riccati type differential equation. We introduce the concepts of minimal and principal solutions of these equations and using these concepts we prove a new ...
Ondrej Dosly, J. Reznickova
doaj +1 more source
On Some Novel Results About the Behavior of Some Numerical Solutions of a Neutrosophic Generalized Half – Linear Second Order Differential Equation [PDF]
Neutrosophic Sets and SystemsThe generalized neutrosophic differential equation is a differential equation with neutrosophic real variable x + yI instead of classical real variable x. This research is devoted to studying the oscillation of generalized neutrosophic half linear second
Norah Mousa Alrayes +5 more
doaj +1 more source
Local estimates for modified Riccati equation in theory of half-linear differential equation
Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper we study the half-linear differential equation \begin{equation*} \bigl(r(t)\Phi_p(x')\bigr)'+c(t)\Phi_p(x)=0, \end{equation*} where $\Phi_p(x)=|x|^{p-2}x$, $p>1$. Using modified Riccati technique and suitable local estimates for terms
Simona Fišnarová, Robert Marik
doaj +1 more source
Modified Riccati technique for half-linear differential equations with delay
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear ...
Simona Fišnarová, Robert Marik
doaj +1 more source
On the integral characterization of principal solutions for half-linear ODE
Electronic Journal of Qualitative Theory of Differential Equations, 2013 We discuss a new integral characterization of principal solutions for half-linear differential equations, introduced in the recent paper of S. Fisnarova and R. Marik, Nonlinear Anal. 74 (2011), 6427-6433.
M. Cecchi +3 more
doaj +1 more source
Principal solution of half-linear differential equation: Limit and integral characterization
Electronic Journal of Qualitative Theory of Differential Equations, 2008 We investigate integral and limit characterizations of the principal solution of the nonoscillatory half-linear differential equation $$ (r(t)\Phi(x'))'+c(t)\Phi(x)=0,\quad \Phi(x)=|x|^{p-2},\ p>1 $$.
Zuzana Dosla, Ondrej Dosly
doaj +1 more source
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We study the half-linear neutral differential equation \begin{equation*} \Bigl[r(t)\Phi(z'(t))\Bigr]'+c(t)\Phi(x(\sigma(t)))=0, \qquad z(t)=x(t)+b(t)x(\tau(t)), \end{equation*} where $\Phi(t)=|t|^{p-2}t$.
Simona Fišnarová
doaj +1 more source
New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations
Mathematics, 2021 In this paper, new oscillation criteria for second-order half-linear neutral delay differential equations are established, using a recently developed method of iteratively improved monotonicity properties of a nonoscillatory solution. Our approach allows
Irena Jadlovská
doaj +1 more source
A remark on power comparison theorem for half-linear differential equations [PDF]
Mathematica Bohemica, 2008 Summary: We consider a half-linear second order differential equation which can be viewed as a perturbation of the so-called Riemann-Weber half-linear differential equation. We present a comparison theorem with respect to the power of the half-linearity in the equation under consideration.
Bognár, Gabriella, Došlý, Ondřej
openaire +2 more sources
Oscillation and nonoscillation of second-order half-linear differential equations [PDF]
Journal of Mathematical Sciences, 2013 The paper considers the problem of oscillation and non-oscillation of the second order half-linear differential equation \[ ({|{u'(t)}|}^{\alpha-1}u'(t))'+p(t){|{u'(t)}|}^{\alpha-1}u(t)=0, \] where \(\alpha>0\) is a constant and \(p\in C([0,+\infty),[0,+\infty))\) is an integrable function.
Yong Zhou, Chen, X.W.
openaire +3 more sources