scholarly journals Positivity of a differential operator with nonlocal conditions

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 885-904
Author(s):  
Allaberen Ashyralyev ◽  
Nese Nalbant
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Nonlocal Boundary Conditions ◽  
Nonlocal Boundary Value Problems ◽  
Fractional Spaces

In the present paper, the positivity of the differential operator with nonlocal boundary conditions is established. The structure of fractional spaces is investigated. In applications, we will obtain new coercive inequalities for the solution of local and nonlocal boundary value problems for parabolic equations.

scholarly journals Sign-constancy of Green’s functions for impulsive nonlocal boundary value problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. Domoshnitsky ◽  
Iu. Mizgireva
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Impulsive Differential Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Nonlocal Boundary Conditions ◽  
Nonlocal Boundary Value Problems ◽  
T Tau

Abstract We consider the following second order impulsive differential equation with delays: $$ \textstyle\begin{cases} (Lx)(t)\equiv x''(t)+\sum_{j=1}^{p} a_{j}(t) x'(t-\tau _{j}(t)) + \sum_{j=1}^{p} b_{j}(t) x(t-\theta _{j}(t)) = f(t), \quad t \in [0, \omega ], \\ x(t_{k})=\gamma _{k} x(t_{k}-0), \quad\quad x'(t_{k})=\delta _{k} x'(t_{k}-0), \quad k=1,2,\ldots,r. \end{cases} $${(Lx)(t)≡x″(t)+∑j=1paj(t)x′(t−τj(t))+∑j=1pbj(t)x(t−θj(t))=f(t),t∈[0,ω],x(tk)=γkx(tk−0),x′(tk)=δkx′(tk−0),k=1,2,…,r. In this paper we consider sufficient conditions of nonpositivity of Green’s function for impulsive differential equation with nonlocal boundary conditions.

scholarly journals SOLVABILITY OF BOUNDARY VALUE PROBLEMS WITH TRANSMISSION CONDITIONS FOR DISCONTINUOUS ELLIPTIC DIFFERENTIAL OPERATOR EQUATIONS

2016 ◽  
Vol 12 (1) ◽  
pp. 5842-5857
Author(s):  
Mustafa Kandemir
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Discontinuous Coefficients ◽  
Transmission Conditions ◽  
Elliptic Differential Operator ◽  
Operator Equations

We consider nonlocal boundary value problems which includes discontinuous coefficients elliptic differential operator equations of the second order and nonlocal boundary conditions together with boundary-transmission conditions. We prove coerciveness and Fredholmness for these nonlocal boundary value problems.

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