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VARIATIONAL METHOD AND CONJUGACY CRITERIA FOR HALF-LINEAR DIFFERENTIAL EQUATIONS [PDF]
, 2013 summary:We establish new conjugacy criteria for half-linear second order differential equations. These criteria are based on the relationship between conjugacy of the investigated equation and nonpositivity of the associated energy ...
Chvátal, Martin +3 more
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Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II [PDF]
, 2021 summary:We consider the half-linear differential equation of the form \[ (p(t)|x^{\prime }|^{\alpha }\mathrm{sgn}\,x^{\prime })^{\prime } + q(t)|x|^{\alpha }\mathrm{sgn}\,x = 0\,, \quad t \ge t_{0} \,, \] under the assumption that $p(t)^{-1/\alpha }$ is ...
Naito, Manabu, Manabu Naito
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Asymptotic forms of solutions of perturbed half-linear ordinary differential equations [PDF]
, 2021 summary:Asymptotic forms of solutions of half-linear ordinary differential equation $\big (|u^{\prime }|^{\alpha -1}u^{\prime }\big )^{\prime }= \alpha \big (1+b(t)\big ) |u|^{\alpha -1}u$ are investigated under a smallness condition and some signum ...
Usami, Hiroyuki, Luey, Sokea
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An oscillatory half-linear differential equation [PDF]
, 1997 summary:A second-order half-linear ordinary differential equation of the type $$(|y^{\prime}|^{\alpha-1}y^{\prime})^{\prime}+\alpha q(t)|y|^{\alpha-1}y=0 \leqno{{\rm (1)}}$$ is considered on an unbounded interval.
Tanigawa, Tomoyuki +2 more
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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
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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
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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
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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
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Analysis and numerical solution of a non-standard non-linear integro-differential boundary value problem [PDF]
, 2011 The aim of this thesis is the analytical study and the development of a numerical method to solve a non-linear, integro-differential boundary value problem on the half line which is representative of a class of non-standard integral equations where the ...
Basile, Mariateresa
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Half-linear discrete oscillation theory
Electronic Journal of Qualitative Theory of Differential Equations, 2000 Oscillatory properties of the second order half-linear difference equation $$\Delta(r_k|\Delta y_k|^{\alpha-2}\Delta y_k)+p_k|y_{k+1}|^{\alpha-2}y_{k+1}=0,$$ where $\alpha>1$, are investigated.
Pavel Řehák
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