Published January 1, 2012 | Version v1
Publication Open

Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem

Creators

  • 1. King Mongkut's University of Technology North Bangkok
  • 2. Centre of Excellence in Mathematics

Description

By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problemΔ2u(t-1)+a(t)f(u(t))=0,t∈{1,2,…,T},u(0)=β∑s=1ηu(s),u(T+1)=α∑s=1ηu(s), wherefis continuous,T≥3is a fixed positive integer,η∈{1,2,...,T-1},0<α<(2T+2)/η(η+1),0<β<(2T+2-αη(η+1))/η(2T-η+1),andΔu(t-1)=u(t)-u(t-1). We show the existence of at least one positive solution iffis either superlinear or sublinear.

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

Translated Description (Arabic)

باستخدام نظرية النقطة الثابتة لكراسنوسيلسكي، ندرس وجود حلول إيجابية لمسألة قيمة الجمع الحدية ثلاثية النقاط Δ2u (t-1)+a (t) f (u (t)) = 0، t.،T-1}،0<α<(2T+2)/η(η+1)،0<β<(2T+2-αη(η+1))/η(2T-η+1)،وΔu(t-1)=u(t)-u(t-1). نظهر وجود حل إيجابي واحد على الأقل إذا كانتf إما فوق الخطية أو تحت الخطية.

Translated Description (French)

En utilisant le théorème du point fixe de Krasnoselskii, nous étudions l'existence de solutions positives au problème de la valeur limite de sommation à trois points Δ2u(t-1)+ a (t) f (u(t))=0,t∈{1,2, …, T},u(0)=β∑ s =1ηu(s),u(T+1)=α∑s=1ηu(s), oùfest continu,T≥3est un entier positif fixe,η∈{1,2,...,T-1},0<α<(2T+2)/η(η+1),0<β<(2T+2-αη(η+1))/η(2T-η+1),etΔu(t-1)=u(t)-u(t-1). Nous montrons l'existence d'au moins une solution positive sifest soit superlinéaire soit sublinéaire.

Translated Description (Spanish)

Usando el teorema del punto fijo de Krasnoselskii, estudiamos la existencia de soluciones positivas al problema del valor límite de la suma de tres puntos Δ2u(t-1)+ a (t)f (u(t))=0,t∈{1,2,…, T},u(0)=β∑s=1ηu(s),u(T+1)=α∑s=1ηu(s), dondefes continuo,T≥3es un entero positivo fijo,η∈{1,2,...,T-1},0<α<(2T+2)/η(η+1),0<β<(2T+2-αη(η+1))/η(2T-η+1),yΔu(t-1)=u(t)-u(t-1). Mostramos la existencia de al menos una solución positiva sifes superlineal o sublineal.

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Additional details

Additional titles

Translated title (Arabic)
الحلول الإيجابية لمعادلة الفرق المعممة من الدرجة الثانية مع مشكلة القيمة الحدية التجميعية
Translated title (French)
Solutions positives à une équation de différence de deuxième ordre généralisée avec un problème de valeur limite de sommation
Translated title (Spanish)
Soluciones Positivas a una Ecuación Generalizada de Diferencia de Segundo Orden con Problema de Valor de Límite de Suma

Identifiers

Other
https://openalex.org/W1990904305
DOI
10.1155/2012/569313

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
Thailand

References

  • https://openalex.org/W1523015984
  • https://openalex.org/W1971619733
  • https://openalex.org/W1972748258
  • https://openalex.org/W1998391228
  • https://openalex.org/W2034941069
  • https://openalex.org/W2056484693
  • https://openalex.org/W2113333224