Nonlocal boundary value problems with different kinds of boundary conditions

2021 ◽  
pp. 15-82
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problems

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 Positive solutions of some nonlocal boundary value problems

2003 ◽  
Vol 2003 (18) ◽  
pp. 1047-1060 ◽  
Author(s):  
Gennaro Infante ◽  
J. R. L. Webb
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Point Boundary ◽  
General Behaviour ◽  
Nonlocal Boundary Value Problems ◽  
Existence Of Positive Solutions

We establish the existence of positive solutions of somem-point boundary value problems under weaker assumptions than previously employed. In particular, we do not require all the parameters occurring in the boundary conditions to be positive. Our results allow more general behaviour for the nonlinear term than being either sub- or superlinear.

scholarly journals The existence of multiple positive solutions of p-Laplacian boundary value problems

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Nonlocal Boundary Value Problems

AbstractIn this paper, we establish sufficient conditions to guarantee the existence of at least three or 2n − 1 positive solutions of nonlocal boundary value problems consisting of the second-order differential equation with p-Laplacian (1) $$[\phi _p (x'(t))]' + f(t,x(t)) = 0, t \in (0,1),$$ and one of following boundary conditions (2) $$x(0) = \int\limits_0^1 {x(s) dh(s),} \phi _p (x'(1)) = \int\limits_0^1 {\phi _p (x'(s)) dg(s)} ,$$ and (3) $$\phi _p (x'(0)) = \int\limits_0^1 {\phi _p (x'(s)) dh(s),} x(1) = \int\limits_0^1 {x(s) dg(s)} .$$ Examples are presented to illustrate the main results.

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.

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