On the question of extended convexity of Green operator
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 26-31
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Let $Q$ be a differential operator of order $m-1$, $2\leqslant m \leqslant n$, for which $(a, b)$ is the interval of nonoscillation, and the Green's operator $G\colon L[a, b]\to W^n[a, b]$ of boundary value problem $Lx=f$, $l_i(x)=0$, $i=1,\dots,n$ has the property of generalized convexity: $QGP>0$ for some linear homeomorphism $P$ of Lebesgue space $L[a,b]$. Under some conditions, we prove, that the perturbed boundary value problem $Lx=PVQx+f$, $l_i(x)=0$, $i=1,\dots,n$ is also uniquely solvable in the Sobolev space $W^n[a,b]$ and the Green's operator $\widehat G$ inherits the property of $G$, that is $Q\widehat GP>0$.
Keywords:
Green's operator, extended convexity.
@article{VUU_2012_1_a2,
author = {G. G. Islamov},
title = {On the question of extended convexity of {Green} operator},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {26--31},
publisher = {mathdoc},
number = {1},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2012_1_a2/}
}
G. G. Islamov. On the question of extended convexity of Green operator. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 26-31. http://geodesic.mathdoc.fr/item/VUU_2012_1_a2/