Abstract and Applied Analysis
Volume 6 (2001), Issue 1, Pages 53-61

Coercive solvability of the nonlocal boundary value problem for parabolic differential equations

A. Ashyralyev,1,2 A. Hanalyev,3 and P. E. Sobolevskii4

1Department of Mathematics, Fatih University, Istanbul, Turkey
2International Turkmen-Turkish University, Ashgabat, Turkmenistan
3Department of AppliedMathematics, Turkmen State University, Ashgabat, Turkmenistan
4Institute of Mathematics, Hebrew University, Jerusalem, Israel

Received 26 March 2001

Copyright © 2001 A. Ashyralyev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The nonlocal boundary value problem, v(t)+Av(t)=f(t)(0t1),v(0)=v(λ)+μ(0<λ1), in an arbitrary Banach space E with the strongly positive operator A, is considered. The coercive stability estimates in Hölder norms for the solution of this problem are proved. The exact Schauder's estimates in Hölder norms of solutions of the boundary value problem on the range {0t1,xn} for 2m-order multidimensional parabolic equations are obtaine.