1. CMB 2011 (vol 56 pp. 39)
|Comparison Theorem for Conjugate Points of a Fourth-order Linear Differential Equation|
In 1961, J. Barrett showed that if the first conjugate point $\eta_1(a)$ exists for the differential equation $(r(x)y'')''= p(x)y,$ where $r(x)\gt 0$ and $p(x)\gt 0$, then so does the first systems-conjugate point $\widehat\eta_1(a)$. The aim of this note is to extend this result to the general equation with middle term $(q(x)y')'$ without further restriction on $q(x)$, other than continuity.
Keywords:fourth-order linear differential equation, conjugate points, system-conjugate points, subwronskians
Categories:47E05, 34B05, 34C10
2. CMB 2011 (vol 55 pp. 3)
|On a Local Theory of Asymptotic Integration for Nonlinear Differential Equations|
We improve several recent results in the asymptotic integration theory of nonlinear ordinary differential equations via a variant of the method devised by J. K. Hale and N. Onuchic The results are used for investigating the existence of positive solutions to certain reaction-diffusion equations.
Keywords:asymptotic integration, Emden-Fowler differential equation, reaction-diffusion equation
Categories:34E10, 34C10, 35Q35
3. CMB 2009 (vol 53 pp. 193)
|On the Oscillation of a Second Order Strictly Sublinear Differential Equation|
We establish a flexible oscillation criterion based on an averaging technique that improves upon a result due to C.~G. Philos.
Keywords:oscillation theory, averaging method
Categories:34C10, 34C15, 34C29