Title: Solvability of multi-point value problems with integral condition at resonance
Author(s): Rabah Khaldi, Mohammed Kouidri
Pages: 306-316
Cite as:
Rabah Khaldi, Mohammed Kouidri, Solvability of multi-point value problems with integral condition at resonance, Int. J. Anal. Appl., 16 (3) (2018), 306-316.

Abstract


In this paper, we study a boundary value problem at resonance with a multi-integral boundary conditions. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. An example is given to show the effectiveness of our results.

Full Text: PDF

 

References


  1. A. Guezane-Lakoud and A. Frioui, Third Order Boundary Value Problem with Integral Condition at Resonance, Math. Comput. Sci. 3 (1) (2013) 56-64. Google Scholar

  2. A. Guezane Lakoud, R. Khaldi and A. Kılı¸ cman, Solvability of a boundary value problem at resonance, Springer Plus 5 (2016), Art. ID 1504. Google Scholar

  3. A. Guezane-Lakoud, N. Hamidane and R. Khaldi, On a third-order three-point boundary value problem. Int. J. Math. Math. Sci. 2012 (2012), Art. ID 513189. Google Scholar

  4. A. Guezane-Lakoud, R. Khaldi, Study of a third-order three-point boundary value problem, AIP Conf. Proc., 1309(2010), 329-335. Google Scholar

  5. C. P. Gupta, Solvability of multi-point boundary value problems at resonance, Results Math. 28(1995), 270-276. Google Scholar

  6. C. P. Gupta, A second order m-point boundary value problem at resonance, Nonlinear Anal. 24 (1995), 1483-1489. Google Scholar

  7. C. P. Gupta, Existence theorems for a second order m-point boundary value problem at resonance, Internat. J. Math. Math. Sci. 18 (1995), no. 4, 705-710. Google Scholar

  8. N. Kosmatov, A multi-point boundary value problem with two critical conditions. Nonlinear Anal. 65 (2006), no. 3, 622–633. Google Scholar

  9. S. K. Ntouyas and P. Ch. Tsamatos, Multi-point boundary value problems for ordinary differential equations. An. S¸tiint ¸. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 45 (1999), no. 1, 57–64 (2000). Google Scholar

  10. Lin, X., Z. Du. and F. Meng, A note on a third-order multi-point boundary value problem at resonance. Math. Nachr. 284 (2011), 1690 – 1700. Google Scholar

  11. R. Ma, Multiplicity results for a third order value problem at resonance, Nonlinear Anal. 32 (1998), no. 4, 493–499. Google Scholar

  12. R. K. Nagle and K. L. Pothoven, On a third-order nonlinear boundary value problems at resonance, J. Math. Anal. Appl. 195 (1995), no 1, 148-159. Google Scholar

  13. J. Mawhin, Topological degree methods in nonlinear boundary value problems. Expository lectures from the CBMS Regional Conference held at Harvey Mudd College, Claremont, Calif., June 9–15, 1977. CBMS Regional Conference Series in Mathematics, 40. American Mathematical Society, Providence, R.I., 1979. Google Scholar

  14. Mawhin, J. Topological degree and boundary value problems for nonlinear differential equations. Topological methods for ordinary differential equations (Montecatini Terme, 1991), 74–142, Lecture Notes in Math., 1537, Springer, Berlin, 1993. Google Scholar


COPYRIGHT INFORMATION

Copyright © 2021 IJAA, unless otherwise stated.