Octavian G. Mustafa
Asymptotically linear solutions of differential equations via Lyapunov functions.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: Octavian G. Mustafa, Cemil Tunc
Subjects: Classical Analysis and ODEs
AbstractWe discuss the existence of solutions with oblique asymptotes to a class of
second order nonlinear ordinary differential equations by means of Lyapunov
functions. The approach is new in this field and allows for simpler proofs of
general results regarding Emden-Fowler like equations.On the asymptotic integration of a class of sublinear fractional differential equations.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: Dumitru Baleanu, Octavian G. Mustafa
Subjects: Dynamical Systems
AbstractWe estimate the growth in time of the solutions to a class of nonlinear
fractional differential equations $D_{0+}^{\alpha}(x-x_0) =f(t,x)$ which
includes $D_{0+}^{\alpha}(x-x_0) =H(t)x^{\lambda}$ with $\lambda\in(0,1)$ for
the case of slowly-decaying coefficients $H$. The proof is based on the triple
interpolation inequality on the real line and the growth estimate reads as
$x(t)=o(t^{a\alpha})$ when $t\to+\infty$ for $1>\alpha>1-a>\lambda>0$.Oscillatory solutions of some perturbed second order differential equations.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: Octavian G. Mustafa
Subjects: Classical Analysis and ODEs
AbstractWe discuss the occurrence of oscillatory solutions which decay to 0 as
$s\to+\infty$ for a class of perturbed second order ordinary differential
equations. As opposed to other results in the recent literature, the
perturbation is as small as desired in terms of its improper integrals and it
is independent of the coefficients of the non-oscillatory unperturbed equation.
This class of equations reveals thus a new pathology in the theory of perturbed
oscillations.Positive solutions of some elliptic differential equations with oscillating nonlinearity.
Thu, 01/07/2010 - 16:01 — SomNambulAuthors: Fahd Jarad, Octavian G. Mustafa, Donal O'Regan
Subjects: Analysis of PDEs
AbstractWe discuss the occurrence of positive solutions which decay to 0 as $|
x|\to+\infty$ to the differential equation $\Delta u+f(x,u)+g(| x|)x\cdot\nabla
u=0$, $| x|>R>0$, $x\in\mathbb{R}^{n}$, where $n\geq 3$, $g$ is nonnegative
valued and $f$ has alternating sign, by means of the comparison method. Our
results complement several recent contributions from [M. Ehrnstr\"{o}m, O.G.
Mustafa, On positive solutions of a class of nonlinear elliptic equations,
Nonlinear Anal. TMA 67 (2007), 1147--1154].
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