Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 04, pp. 1-23.
Title: On Oleck-Opial-Beesack-Troy integro-differential inequalities
Authors: Evgeniy I. Bravyi (Perm State Technical Univ., Russia)
Sergey S. Gusarenko (Perm State University, Russia)
Abstract:
We obtain necessary and sufficient conditions for the
integro-differential inequality
$$
\int_a^b\dot x^2(t)\,dt\geq\gamma\int_a^bq(t)\,|\dot x(t)x(t)|\,dt
$$
to be valid with one of the three boundary conditions: $x(a)=0$,
or $x(a)=0$, or $x(a)=x(b)=0$. For a power functions $q$, the best constants
$\gamma$ are found.
Submitted October 27, 2003. Published January 2, 2004.
Math Subject Classifications: 34K10, 34B30, 34B05, 41A44, 49J40, 58E35.
Key Words: Integral inequalities; integro-differential inequalities;
functional differential equations; variational problems.