Dear Colleagues,

                        We continue our Colloquium at the Math
Department


                Zuzana Dosla

Masaryk University, Brno, Czech Republic

Thursday, October 9, EMCS 422, 3:00pm.

ON PRINCIPAL SOLUTIONS OF HALF-LINEAR DIFFERENTIAL EQUATIONS

Abstract

We present some recent results for the half-linear differential equation

$$(a(t)\Phi_{p}(x^{\prime}))^{\prime}=b(t)\Phi_{p}(x)
(E)$$

where the functions $a(t)$ and $b(t)$ are continuous, $a(t)>0,$ and
$\Phi_p(u)=|u|^{p-2}u$ with $p>1.$

The notion of principal solution of the nonoscillatory linear equation
was introduced by W. Leighton, M. Morse and P. Hartman as a "smallest
solution in a neighborhood of infinity." Following the Riccati equation
approach, the notion of principal solution has been extended to (E)
independently by J. Mirzov and by A. Elbert $\&$ T. Kusano. We show that
the limit and integral characterizations of principal solutions hold for
(E) as well.


Students are encouraged to attend.


Boris P Belinskiy

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748