Skip to main content
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2016

01.02.2016 | Original Research

Existence of positive solutions for a fourth-order three-point boundary value problem

verfasst von: A. Guezane-Lakoud, L. Zenkoufi

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2016

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we are concerned with a fourth-order three point boundary value problem. We prove the existence, uniqueness and positivity of solutions by using Leray–Schauder nonlinear alternative, Banach contraction theorem and Guo–Krasnosel’skii fixed point theorem.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Anderson, D.R.: Green’s function for a third-order generalized right focal problem. J. Math. Anal. Appl. 288, 1–14 (2003)MathSciNetCrossRefMATH Anderson, D.R.: Green’s function for a third-order generalized right focal problem. J. Math. Anal. Appl. 288, 1–14 (2003)MathSciNetCrossRefMATH
2.
Zurück zum Zitat Agarwal, R.P., O’Regan, D., Wong, P.: Positive Solutions of Differential Equations, Difference, and Integral Equations. Kluwer Academic, Boston (1999)CrossRefMATH Agarwal, R.P., O’Regan, D., Wong, P.: Positive Solutions of Differential Equations, Difference, and Integral Equations. Kluwer Academic, Boston (1999)CrossRefMATH
3.
Zurück zum Zitat Bai, Z., Wang, H.: On positive solutions of some nonliear fourth-order beam equations. J. Math. Anal. Appl. 270, 357–368 (2002)MathSciNetCrossRefMATH Bai, Z., Wang, H.: On positive solutions of some nonliear fourth-order beam equations. J. Math. Anal. Appl. 270, 357–368 (2002)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Chen, J., Tariboon, J., Koonprasert, S.: Existence of positive solutions to a second-order multi-point boundary value problem with delay, Thai J. Math. Special Issue (Annual Meeting in Mathematics, 2010): 21–32 (2010) Chen, J., Tariboon, J., Koonprasert, S.: Existence of positive solutions to a second-order multi-point boundary value problem with delay, Thai J. Math. Special Issue (Annual Meeting in Mathematics, 2010): 21–32 (2010)
6.
Zurück zum Zitat Graef, J.R., Henderson, Yang, B.: Positive solutions of a nonlinear nth order eigenvalue problem. Dyn. Contin. Discret. Impuls. Syst. Ser. A Math. Anal. 13B(Supplementary Volume), 39–48 (2006)MathSciNet Graef, J.R., Henderson, Yang, B.: Positive solutions of a nonlinear nth order eigenvalue problem. Dyn. Contin. Discret. Impuls. Syst. Ser. A Math. Anal. 13B(Supplementary Volume), 39–48 (2006)MathSciNet
7.
Zurück zum Zitat Graef, J.R., Henderson, Wong, P.J.Y.: Three solutions of an nth order three-point focal type boundary value problem. Nonlinear Anal. 69, 3386–3404 (2008)MathSciNetCrossRefMATH Graef, J.R., Henderson, Wong, P.J.Y.: Three solutions of an nth order three-point focal type boundary value problem. Nonlinear Anal. 69, 3386–3404 (2008)MathSciNetCrossRefMATH
8.
Zurück zum Zitat Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, San Diego (1988)MATH Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, San Diego (1988)MATH
9.
Zurück zum Zitat Guezane-Lakoud, A., Frioui, A.: Nonlinear three-point boundary-value problem. Sarajevo J. Math. 8(20), 1–6 (2012)MathSciNetMATH Guezane-Lakoud, A., Frioui, A.: Nonlinear three-point boundary-value problem. Sarajevo J. Math. 8(20), 1–6 (2012)MathSciNetMATH
10.
Zurück zum Zitat Guezane-Lakoud, A., Hamidane, N., Khaldi, R.: On a third order three-point boundary value problem, Int. J. Math. Sci. Art. ID 513189, 7pp (2012) Guezane-Lakoud, A., Hamidane, N., Khaldi, R.: On a third order three-point boundary value problem, Int. J. Math. Sci. Art. ID 513189, 7pp (2012)
11.
Zurück zum Zitat Guezane-Lakoud, A., Zenkoufi, L.: Existence of positive solutions for a third order multi-point boundary value problem. Appl. Math. 3, 1008–1013 (2013)CrossRefMATH Guezane-Lakoud, A., Zenkoufi, L.: Existence of positive solutions for a third order multi-point boundary value problem. Appl. Math. 3, 1008–1013 (2013)CrossRefMATH
12.
Zurück zum Zitat Le, X.Truong, Phan Fhung, D.: Existence of positive solutions for a multi-point four-order boundary value problem. Electron. J. Differ. Equ. 2011, 1–10 (2011)MathSciNet Le, X.Truong, Phan Fhung, D.: Existence of positive solutions for a multi-point four-order boundary value problem. Electron. J. Differ. Equ. 2011, 1–10 (2011)MathSciNet
13.
Zurück zum Zitat Li, Y.: Positive solutions of fourth-order boundary value problems with two parameters. J. Math. Anal. Appl. 281, 477–484 (2003)MathSciNetCrossRefMATH Li, Y.: Positive solutions of fourth-order boundary value problems with two parameters. J. Math. Anal. Appl. 281, 477–484 (2003)MathSciNetCrossRefMATH
14.
Zurück zum Zitat Li, Y.: On the existence of positive solutions for the bending elastic beam equations. Appl. Math. Comput. 189, 821–827 (2007)MathSciNetCrossRefMATH Li, Y.: On the existence of positive solutions for the bending elastic beam equations. Appl. Math. Comput. 189, 821–827 (2007)MathSciNetCrossRefMATH
15.
16.
Zurück zum Zitat Ma, R.: Multiple positive solutions for semipositone fourth-order boundary value problem. Hirochima Math. J. 33, 217–227 (2003)MATHMathSciNet Ma, R.: Multiple positive solutions for semipositone fourth-order boundary value problem. Hirochima Math. J. 33, 217–227 (2003)MATHMathSciNet
17.
Zurück zum Zitat Ma, R., Wang, H.: On the existence of positive solutions of fourth-order ordinary differential equations. Appl. Anal. 59, 225–231 (1995)MathSciNetCrossRefMATH Ma, R., Wang, H.: On the existence of positive solutions of fourth-order ordinary differential equations. Appl. Anal. 59, 225–231 (1995)MathSciNetCrossRefMATH
18.
Zurück zum Zitat Yong-ping, Sun: Existence and multiplicity of positive solutions for an elastic beam equation. Appl. Math. J. Chin. Univ. 26(3), 253–264 (2011)CrossRefMathSciNet Yong-ping, Sun: Existence and multiplicity of positive solutions for an elastic beam equation. Appl. Math. J. Chin. Univ. 26(3), 253–264 (2011)CrossRefMathSciNet
19.
Zurück zum Zitat Wang, W., Shen, J.: Positive solutions to a multi-point boundary value problem with delay. Appl. Math. Comput. 188, 96–102 (2007)MathSciNetCrossRefMATH Wang, W., Shen, J.: Positive solutions to a multi-point boundary value problem with delay. Appl. Math. Comput. 188, 96–102 (2007)MathSciNetCrossRefMATH
20.
Zurück zum Zitat Webb, J.R.L.: Positive solutions of some three-point boundary value problems via fixed point index theory. Nonlinear Anal. 47, 4319–4332 (2001)MathSciNetCrossRefMATH Webb, J.R.L.: Positive solutions of some three-point boundary value problems via fixed point index theory. Nonlinear Anal. 47, 4319–4332 (2001)MathSciNetCrossRefMATH
21.
Zurück zum Zitat Sun, Y., Zhu, C.: Existence of positive solutions for singular fourth-order three-point boundary value problems. Adv. Differ. Equ. 2013(51), 1–13 (2013)MathSciNet Sun, Y., Zhu, C.: Existence of positive solutions for singular fourth-order three-point boundary value problems. Adv. Differ. Equ. 2013(51), 1–13 (2013)MathSciNet
22.
Zurück zum Zitat Yang, Y.R.: Triple positive solution of a class of fourth-order two-point boundary value problems. Appl. Math. Lett. 23, 366–370 (2010)MathSciNetCrossRefMATH Yang, Y.R.: Triple positive solution of a class of fourth-order two-point boundary value problems. Appl. Math. Lett. 23, 366–370 (2010)MathSciNetCrossRefMATH
23.
Zurück zum Zitat Zhang, X., Lishan, L., Congxin, W.: Nontrivial solution of third-order nonlinear eigenvalue problems (II). Appl. Math. Comput. 176, 714–721 (2006)MathSciNetCrossRefMATH Zhang, X., Lishan, L., Congxin, W.: Nontrivial solution of third-order nonlinear eigenvalue problems (II). Appl. Math. Comput. 176, 714–721 (2006)MathSciNetCrossRefMATH
24.
Zurück zum Zitat Zhang, X., Lishan, L.: Nontrivial solution of third-order nonlinear eigenvalue problems (II). Appl. Math. Comput. 204, 508–512 (2008)MathSciNetCrossRefMATH Zhang, X., Lishan, L.: Nontrivial solution of third-order nonlinear eigenvalue problems (II). Appl. Math. Comput. 204, 508–512 (2008)MathSciNetCrossRefMATH
Metadaten
Titel
Existence of positive solutions for a fourth-order three-point boundary value problem
verfasst von
A. Guezane-Lakoud
L. Zenkoufi
Publikationsdatum
01.02.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2016
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-014-0863-5

Weitere Artikel der Ausgabe 1-2/2016

Journal of Applied Mathematics and Computing 1-2/2016 Zur Ausgabe