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EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM

Year 2013, Volume: 62 Issue: 1, 121 - 129, 01.02.2013
https://doi.org/10.1501/Commua1_0000000691

Abstract

This paper deals with a second order boundary value problem withonly integrals conditions. Our aim is to give new conditions on the nonlinearterm; then, using Banach contraction principle and Leray Schauder nonlinearalternative, we establish the existence of nontrivial solution of the consideredproblem. As an application, some examples to illustrate our results are given

References

  • R.A. Agarwal and D. O’Regan, In…nite interval problems modelling phenomena which arise in the theory of plasma and electrical theory , Studies. Appl. Math. 111 (2003) 339–358.
  • D.R. Anderson, Green’s function for a third-order generalized right focal problem, J. Math. Anal. Appl. 288 (2003), 1–14.
  • M. Benchohra, J.J. Nieto and A. Ouahab, Second-order boundary value problem with integral boundary conditions, Bound. Value Probl. 2011, ID 260309, 9 pages.
  • K. Deimling, Non-linear Functional Analysis, Springer, Berlin, 1985.
  • H. Fan and R. Ma, Loss of positivity in a nonlinear second order ordinary diğ erential equa- tions, Nonlinear Anal. 71 (2009), 437–444.
  • J.R. Graef, Bo Yang, Existence and nonexistence of positive solutions of a nonlinear third order boundary value problem, Electronic Journal of Qualitative Theory of Diğerential Equa- tions Proc. 8th Coll. QTDE, 2008, No. 9, 1–13.
  • A. Guezane-Lakoud, N. Hamidane and R. Khaldi, Existence and positivity of solutions for a second order boundary value problem with integral condition, Int. J. Diğer. Equ. 2012, ID , 14 pages.
  • A. Guezane-Lakoud, N. Hamidane and R. Khaldi, On a third-order three-point boundary value problem. Int. J. Math. Math. Sci. 2012, ID 513189, 7 pages.
  • C.P. Gupta, Solvability of a three-point nonlinear boundary value problem for a second order diğ erential equation, J. Math. Anal. Appl. 168 (1992), 540–551.
  • L.J. Guo, J.P. Sun and Y.H. Zhao, Existence of positive solutions for nonlinear third-order three-point boundary value problem, Nonlinear Anal. 68 (10) (2008), 3151–3158.
  • B. Hopkins and N. Kosmatov, Third-order boundary value problems with sign changing so- lutions, Nonlinear Analysis, 67, 1 (2007) 126–137.
  • R.A. Khan and N.A. Asif, Positive solutions for a class of singular two point boundary value problems, J. Nonlinear. Sci. Appl. 2 (2009), no 2, 126–135
  • S. Li, Positive solutions of nonlinear singular third-order two-point boundary value problem, J. Math. Anal. Appl. 323 (2006), 413–425.
  • R. Ma, A survey on nonlocal boundary value problems. Appl. Math. E-Notes 7 (2007), 257–
  • L. Shuhong and Y-P. Sun, Nontrivial solution of a nonlinear second order three point bound- ary value problem, Appl. Math. J. 22 (1) (2007), 37-47.
  • Current address : A. Guezane-Lakoud and N. Hamidane;Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000, Annaba, ALGERIA.
  • R. Khaldi; Laboratory LASEA, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box , 23000, Annaba, ALGERIA.
  • E-mail address : a_guezane@yahoo.fr; nhamidane@yahoo.com, rkhadi@yahoo.fr URL: http://communications.science.ankara.edu.tr/index.php?series=A1
Year 2013, Volume: 62 Issue: 1, 121 - 129, 01.02.2013
https://doi.org/10.1501/Commua1_0000000691

Abstract

References

  • R.A. Agarwal and D. O’Regan, In…nite interval problems modelling phenomena which arise in the theory of plasma and electrical theory , Studies. Appl. Math. 111 (2003) 339–358.
  • D.R. Anderson, Green’s function for a third-order generalized right focal problem, J. Math. Anal. Appl. 288 (2003), 1–14.
  • M. Benchohra, J.J. Nieto and A. Ouahab, Second-order boundary value problem with integral boundary conditions, Bound. Value Probl. 2011, ID 260309, 9 pages.
  • K. Deimling, Non-linear Functional Analysis, Springer, Berlin, 1985.
  • H. Fan and R. Ma, Loss of positivity in a nonlinear second order ordinary diğ erential equa- tions, Nonlinear Anal. 71 (2009), 437–444.
  • J.R. Graef, Bo Yang, Existence and nonexistence of positive solutions of a nonlinear third order boundary value problem, Electronic Journal of Qualitative Theory of Diğerential Equa- tions Proc. 8th Coll. QTDE, 2008, No. 9, 1–13.
  • A. Guezane-Lakoud, N. Hamidane and R. Khaldi, Existence and positivity of solutions for a second order boundary value problem with integral condition, Int. J. Diğer. Equ. 2012, ID , 14 pages.
  • A. Guezane-Lakoud, N. Hamidane and R. Khaldi, On a third-order three-point boundary value problem. Int. J. Math. Math. Sci. 2012, ID 513189, 7 pages.
  • C.P. Gupta, Solvability of a three-point nonlinear boundary value problem for a second order diğ erential equation, J. Math. Anal. Appl. 168 (1992), 540–551.
  • L.J. Guo, J.P. Sun and Y.H. Zhao, Existence of positive solutions for nonlinear third-order three-point boundary value problem, Nonlinear Anal. 68 (10) (2008), 3151–3158.
  • B. Hopkins and N. Kosmatov, Third-order boundary value problems with sign changing so- lutions, Nonlinear Analysis, 67, 1 (2007) 126–137.
  • R.A. Khan and N.A. Asif, Positive solutions for a class of singular two point boundary value problems, J. Nonlinear. Sci. Appl. 2 (2009), no 2, 126–135
  • S. Li, Positive solutions of nonlinear singular third-order two-point boundary value problem, J. Math. Anal. Appl. 323 (2006), 413–425.
  • R. Ma, A survey on nonlocal boundary value problems. Appl. Math. E-Notes 7 (2007), 257–
  • L. Shuhong and Y-P. Sun, Nontrivial solution of a nonlinear second order three point bound- ary value problem, Appl. Math. J. 22 (1) (2007), 37-47.
  • Current address : A. Guezane-Lakoud and N. Hamidane;Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box 12, 23000, Annaba, ALGERIA.
  • R. Khaldi; Laboratory LASEA, Faculty of Sciences, Badji Mokhtar-Annaba University, P.O. Box , 23000, Annaba, ALGERIA.
  • E-mail address : a_guezane@yahoo.fr; nhamidane@yahoo.com, rkhadi@yahoo.fr URL: http://communications.science.ankara.edu.tr/index.php?series=A1
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

A. Guezane-lakoud This is me

N. Hamidane This is me

R. Khaldi This is me

Publication Date February 1, 2013
Published in Issue Year 2013 Volume: 62 Issue: 1

Cite

APA Guezane-lakoud, A., Hamidane, N., & Khaldi, R. (2013). EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 62(1), 121-129. https://doi.org/10.1501/Commua1_0000000691
AMA Guezane-lakoud A, Hamidane N, Khaldi R. EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2013;62(1):121-129. doi:10.1501/Commua1_0000000691
Chicago Guezane-lakoud, A., N. Hamidane, and R. Khaldi. “EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62, no. 1 (February 2013): 121-29. https://doi.org/10.1501/Commua1_0000000691.
EndNote Guezane-lakoud A, Hamidane N, Khaldi R (February 1, 2013) EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62 1 121–129.
IEEE A. Guezane-lakoud, N. Hamidane, and R. Khaldi, “EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 62, no. 1, pp. 121–129, 2013, doi: 10.1501/Commua1_0000000691.
ISNAD Guezane-lakoud, A. et al. “EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 62/1 (February 2013), 121-129. https://doi.org/10.1501/Commua1_0000000691.
JAMA Guezane-lakoud A, Hamidane N, Khaldi R. EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62:121–129.
MLA Guezane-lakoud, A. et al. “EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 62, no. 1, 2013, pp. 121-9, doi:10.1501/Commua1_0000000691.
Vancouver Guezane-lakoud A, Hamidane N, Khaldi R. EXISTENCE AND UNIQUENESS OF SOLUTION FOR A SECOND ORDER BOUNDARY VALUE PROBLEM. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2013;62(1):121-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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