Solvability of multi-point value problems with integral condition at resonance

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

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Rabah Khaldi, Mohammed Kouidri

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.

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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.
  2. A. Guezane Lakoud, R. Khaldi and A. Kili ¸ cman, Solvability of a boundary value problem at resonance, Springer Plus 5 (2016), Art. ID 1504.
  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.
  4. A. Guezane-Lakoud, R. Khaldi, Study of a third-order three-point boundary value problem, AIP Conf. Proc., 1309(2010), 329-335.
  5. C. P. Gupta, Solvability of multi-point boundary value problems at resonance, Results Math. 28(1995), 270-276.
  6. C. P. Gupta, A second order m-point boundary value problem at resonance, Nonlinear Anal. 24 (1995), 1483-1489.
  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.
  8. N. Kosmatov, A multi-point boundary value problem with two critical conditions. Nonlinear Anal. 65 (2006), no. 3, 622-633.
  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).
  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.
  11. R. Ma, Multiplicity results for a third order value problem at resonance, Nonlinear Anal. 32 (1998), no. 4, 493-499.
  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.
  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.
  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.