International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1993 / Article

Open Access

Volume 6 |Article ID 590323 | https://doi.org/10.1155/S1048953393000115

Yunfeng Yin, "Quasilinearization for some nonlocal problems", International Journal of Stochastic Analysis, vol. 6, Article ID 590323, 6 pages, 1993. https://doi.org/10.1155/S1048953393000115

Quasilinearization for some nonlocal problems

Received01 Feb 1993
Revised01 Apr 1993

Abstract

The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation utLu=f(t,x,u) with nonlocal boundary conditions u(t,x)=Ωϕ(x,y)u(t,y)dy in this paper. The convexity of f in u is relaxed by requiring f(t,x,u)+Mu2 to be convex for some M>0. The quadratic convergence of monotone sequence is obtained.

Copyright © 1993 Hindawi Publishing Corporation. 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.


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