Published January 1, 2012 | Version v1
Publication Open

Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation

Creators

  • 1. Alexandria University
  • 2. University of Benghazi

Description

We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equationx′′(t)=f(t,x(ϕ(t))),t∈(0,1), with the nonlocal condition∑k=1makx(τk)=x0,x′(0)+∑j=1nbjx′(ηj)=x1, whereτk∈(a,d)⊂(0,1),ηj∈(c,e)⊂(0,1), andx0,x1>0. As an application the integral and the nonlocal conditions∫adx(t)dt=x0,x′(0)+x(e)-x(c)=x1will be considered.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

ندرس وجود حل إيجابي رتيب واحد على الأقل لمشكلة القيمة الحدية غير المحلية للمعادلة التفاضلية الوظيفية من الدرجة الثانية x′ ′( t)= f (t, x ( كتطبيق، سيتم النظر في الشروط المتكاملة وغير المحلية (أ) dx(t)dt=x0،x′( 0)+x(e)-x(c)=x1.

Translated Description (French)

Nous étudions l'existence d'au moins une solution positive monotone pour le problème de valeur limite non locale de l'équation différentielle fonctionnelle du deuxième ordre x′′(t)=f (t,x (ϕ(t))), t∈(0,1), avec la condition non locale ∑k=1m a k x(τ k)= x 0,x′(0)+∑j=1nb j x′(η j)=x1, oùτk∈(a,d) (0,1),ηj∈(c,e) (0,1), etx0,x1>0. En tant qu'application, les conditions intégrales et non locales ∫adx(t)dt=x0,x′(0)+x(e)-x(c)=x1seront considérées.

Translated Description (Spanish)

Estudiamos la existencia de al menos una solución positiva monótona para el problema del valor límite no local de la ecuación diferencial funcional de segundo orden x′′(t)=f(t,x(ϕ(t))),t∈(0,1), con la condición no local ∑k=1m a kx(τ k)=x0,x′(0)+∑j=1nbjx′(ηj)=x1, dondeτk∈(a,d). (0,1),ηj∈(c,e). (0,1), yx0,x1>0. Como aplicación, se considerarán las condiciones integrales y no locales a dx(t)dt=x0,x′(0)+x(e)- x (c)=x1.

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Additional details

Additional titles

Translated title (Arabic)
حلول إيجابية رتيبة لمشاكل القيمة الحدية غير المحلية لمعادلة تفاضلية وظيفية من الدرجة الثانية
Translated title (French)
Solutions positives monotones aux problèmes de valeur limite non locale pour une équation différentielle fonctionnelle de deuxième ordre
Translated title (Spanish)
Soluciones positivas monotónicas de problemas de valores de límites no locales para una ecuación diferencial funcional de segundo orden

Identifiers

Other
https://openalex.org/W2000259918
DOI
10.1155/2012/489353

Is supplement to
https://openalex.org/W4313731559 (Other)
https://openalex.org/W2989452537 (Other)
https://openalex.org/W2544423928 (Other)
https://openalex.org/W2187401768 (Other)
https://openalex.org/W2181743346 (Other)
https://openalex.org/W2181413294 (Other)
https://openalex.org/W2073681303 (Other)
https://openalex.org/W2053286651 (Other)
https://openalex.org/W2052122378 (Other)
https://openalex.org/W2051487156 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Egypt

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