Nonlocal boundary-value problem for parabolic equations

1994 ◽  
Vol 46 (12) ◽  
pp. 1795-1802 ◽  
Author(s):  
N. M. Zadorozhna ◽  
O. M. Mel'nik ◽  
B. I. Ptashnik
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problem

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

2001 ◽  
Vol 6 (1) ◽  
pp. 53-61 ◽  
Author(s):  
A. Ashyralyev ◽  
A. Hanalyev ◽  
P. E. Sobolevskii
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Parabolic Differential Equations ◽  
Coercive Solvability ◽  
Coercive Stability

The nonlocal boundary value problem,v′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ(0<λ≤1), in an arbitrary Banach spaceEwith the strongly positive operatorA, 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{0≤t≤1,xℝ n}for2m-order multidimensional parabolic equations are obtaine.

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

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