Research Article
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Year 2020, , 43 - 54, 12.11.2020
https://doi.org/10.47087/mjm.549174

Abstract

References

  • [1] A. Yong, B. Sun and W. Ge; Existence of positive solutions for self-adjoint boundary valueproblems with integral boundary condition at resonance, Electron. J. Differential Equations.(2011), 11, 1-8.
  • [2] A. Guezane-Lakoud, A. Frioui; Third-order boundary value problem with integral condition atresonance, Theory and Application of Mathematics and Comput Science. 3 (1)(2013), 56-64.
  • [3] B. Przeradzki and R. Stanczy; Solvability of multi-point boundary value problems at reso-nance, J. Math. Anal. Appl. 264 (2001), No. 2, 253261.
  • [4] C. P. Gupta; Solvability of a three-point nonlinear boundary value problem for a second orderordinary differential equations, J. Math. Anal. Appl. 168 (1998), 540{551.[
  • 5] C. Xue, Z. Du and W. Ge; Solutions of M-point boundary value problems of third-orderordinary differential equations at resonance, J. Appl. Math. Comput. 17 (2005), No. 1-2,229{244.
  • [6] E. R. Kaufmann; A third-order nonlocal boundary value problem at resonance, Electron. J.Qual. Theory Differ. Equ. 2009 (2009), No. 16, 1-11.
  • [7] F. Meng and Z. Du; Solvability of a second order multi-point boundary value problems atresonance, Appl. Math. Comput 208, (2010), 23-30.
  • [8] G. Karakostas and P. Ch. Tsamatos; On a nonlocal boundary value problem at resonance, J.Math. Anal. Appl. 259 (2001), No. 1, 209-218.
  • [9] G. Karakostas and P. Ch. Tsamatos; Suffcient conditions for the exsistence of nonnegativesolutions of a nonlocal boundary value problem. Appl. Math. Letters 15(4) (2002), 401{407.
  • [10] H. Zhang. W. Liu and T. Chen; Exsistence of solutions for three-point boundary value prob-lem. J. Appl. Math and Informatics. 27(5-6) (2009), 35{51.
  • [11] H. Z. Wang, Y. Li; Neumann boundary value problems for second-order ordinary differentialequations across resonance, SIAM J. Control Optim. 33 (1995), 1312{1325.
  • [12] J. Mawhin; Tobological degree Methods in Nonlinear Boundary Value Problems, NSF-CBMSRegional Conference Series in Mathematics,40, Amer. Math. Soc., Providence, RI, 1979.
  • [13] J.R.L. Webb, M. Zima; Multiple positive solutions of resonant and non-resonant nonlocalboundary value problems, Nonlinear Anal. 71 (2009) 1369{1378.
  • [14] N. Kosmatov; Multi-point boundary value problems on an unbounded domain at resonance,Nonlinear Anal. 68 (2008), 2158{2171.
  • [15] R. Ma; Suffcient Conditions for the Existence of Nonnegative Solutions of a Nonlocal Bound-ary Value Problem, Appl. Math. Letters 15 (2002) 401{407.
  • [16] R. Ma; Multiplicity results for a third order boundary value problem at resonance, NonlinearAnal. 32 (2005), 493{499.
  • [17] W. Feng and J. R. L. Webb; Solvability of three-point boundary value problem at resonance,Nonlinear Anal. Theory, Methods and Appl 30, (1997) 3227{3238.
  • [18] W. H. Jiang, Y. P. Guo and J. Qiu; Solvability of 2n-order m-point boundary value problemat resonance, Appl. Math. Mech. (English Ed) 28(2007), No. 9, 1219-1226.
  • [19] X. Liu, J. Qiu, Y. Guo; Three positive solutions for second-order m-point boundary valueproblems, Appl. Math. Comput. 156 no. 3 (2004) 733{742
  • [20] X. Zhang, M. Feng and W. Ge; Existence result of second-order differential equations withintegral boundary conditions at resonance, J. Math. Appl. 353 (2009),1, 311-319.
  • [21] Y. Lin, Z. D and F. Meng; A note on third-order multi-point boundary value problem atresonance, Math. Nachr 284 (13) (2011), 1690-1700.
  • [22] Z. Du, W. Ge, X. Lin; Nonlocal boundary value problem of higher order ordinary differentialequations at resonance, Rocky Mountain J. Math. 36 No. 5 (2006), 1471{1486.

A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE

Year 2020, , 43 - 54, 12.11.2020
https://doi.org/10.47087/mjm.549174

Abstract

In this paper, we consider third-order boundary value problem
with, Dirichlet, Neumann and integral conditions at resonance case, where the
kernel’s dimension of the ordinary differential operator is equal to one and the
ordinary differential equation which can be written as the abstract equation
Lu = Nu, called semilinear form, where L is a linear Fredholm operator of
index zero, and N is a nonlinear operator. First, we prove a priori estimates,
and then we use Mawhin’s coincidence degree theory to deduce the existence
of solutions. One important ingredient to be able to apply this abstract results
(Mawhin’s coincidence degree theory) is proving the Fredholm property of the
operator L. An example is also presented to illustrate the effectiveness of the
main results



with integral condition at
resonance case



The existence of solution is
etablished via Mawhin's coincidence degree theory. 
The results are illustrated with an example.

References

  • [1] A. Yong, B. Sun and W. Ge; Existence of positive solutions for self-adjoint boundary valueproblems with integral boundary condition at resonance, Electron. J. Differential Equations.(2011), 11, 1-8.
  • [2] A. Guezane-Lakoud, A. Frioui; Third-order boundary value problem with integral condition atresonance, Theory and Application of Mathematics and Comput Science. 3 (1)(2013), 56-64.
  • [3] B. Przeradzki and R. Stanczy; Solvability of multi-point boundary value problems at reso-nance, J. Math. Anal. Appl. 264 (2001), No. 2, 253261.
  • [4] C. P. Gupta; Solvability of a three-point nonlinear boundary value problem for a second orderordinary differential equations, J. Math. Anal. Appl. 168 (1998), 540{551.[
  • 5] C. Xue, Z. Du and W. Ge; Solutions of M-point boundary value problems of third-orderordinary differential equations at resonance, J. Appl. Math. Comput. 17 (2005), No. 1-2,229{244.
  • [6] E. R. Kaufmann; A third-order nonlocal boundary value problem at resonance, Electron. J.Qual. Theory Differ. Equ. 2009 (2009), No. 16, 1-11.
  • [7] F. Meng and Z. Du; Solvability of a second order multi-point boundary value problems atresonance, Appl. Math. Comput 208, (2010), 23-30.
  • [8] G. Karakostas and P. Ch. Tsamatos; On a nonlocal boundary value problem at resonance, J.Math. Anal. Appl. 259 (2001), No. 1, 209-218.
  • [9] G. Karakostas and P. Ch. Tsamatos; Suffcient conditions for the exsistence of nonnegativesolutions of a nonlocal boundary value problem. Appl. Math. Letters 15(4) (2002), 401{407.
  • [10] H. Zhang. W. Liu and T. Chen; Exsistence of solutions for three-point boundary value prob-lem. J. Appl. Math and Informatics. 27(5-6) (2009), 35{51.
  • [11] H. Z. Wang, Y. Li; Neumann boundary value problems for second-order ordinary differentialequations across resonance, SIAM J. Control Optim. 33 (1995), 1312{1325.
  • [12] J. Mawhin; Tobological degree Methods in Nonlinear Boundary Value Problems, NSF-CBMSRegional Conference Series in Mathematics,40, Amer. Math. Soc., Providence, RI, 1979.
  • [13] J.R.L. Webb, M. Zima; Multiple positive solutions of resonant and non-resonant nonlocalboundary value problems, Nonlinear Anal. 71 (2009) 1369{1378.
  • [14] N. Kosmatov; Multi-point boundary value problems on an unbounded domain at resonance,Nonlinear Anal. 68 (2008), 2158{2171.
  • [15] R. Ma; Suffcient Conditions for the Existence of Nonnegative Solutions of a Nonlocal Bound-ary Value Problem, Appl. Math. Letters 15 (2002) 401{407.
  • [16] R. Ma; Multiplicity results for a third order boundary value problem at resonance, NonlinearAnal. 32 (2005), 493{499.
  • [17] W. Feng and J. R. L. Webb; Solvability of three-point boundary value problem at resonance,Nonlinear Anal. Theory, Methods and Appl 30, (1997) 3227{3238.
  • [18] W. H. Jiang, Y. P. Guo and J. Qiu; Solvability of 2n-order m-point boundary value problemat resonance, Appl. Math. Mech. (English Ed) 28(2007), No. 9, 1219-1226.
  • [19] X. Liu, J. Qiu, Y. Guo; Three positive solutions for second-order m-point boundary valueproblems, Appl. Math. Comput. 156 no. 3 (2004) 733{742
  • [20] X. Zhang, M. Feng and W. Ge; Existence result of second-order differential equations withintegral boundary conditions at resonance, J. Math. Appl. 353 (2009),1, 311-319.
  • [21] Y. Lin, Z. D and F. Meng; A note on third-order multi-point boundary value problem atresonance, Math. Nachr 284 (13) (2011), 1690-1700.
  • [22] Z. Du, W. Ge, X. Lin; Nonlocal boundary value problem of higher order ordinary differentialequations at resonance, Rocky Mountain J. Math. 36 No. 5 (2006), 1471{1486.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Bouteraa Noureddine 0000-0002-8772-1315

Publication Date November 12, 2020
Acceptance Date November 5, 2020
Published in Issue Year 2020

Cite

APA Noureddine, B. (2020). A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE. Maltepe Journal of Mathematics, 2(2), 43-54. https://doi.org/10.47087/mjm.549174
AMA Noureddine B. A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE. Maltepe Journal of Mathematics. November 2020;2(2):43-54. doi:10.47087/mjm.549174
Chicago Noureddine, Bouteraa. “A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE”. Maltepe Journal of Mathematics 2, no. 2 (November 2020): 43-54. https://doi.org/10.47087/mjm.549174.
EndNote Noureddine B (November 1, 2020) A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE. Maltepe Journal of Mathematics 2 2 43–54.
IEEE B. Noureddine, “A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE”, Maltepe Journal of Mathematics, vol. 2, no. 2, pp. 43–54, 2020, doi: 10.47087/mjm.549174.
ISNAD Noureddine, Bouteraa. “A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE”. Maltepe Journal of Mathematics 2/2 (November 2020), 43-54. https://doi.org/10.47087/mjm.549174.
JAMA Noureddine B. A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE. Maltepe Journal of Mathematics. 2020;2:43–54.
MLA Noureddine, Bouteraa. “A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE”. Maltepe Journal of Mathematics, vol. 2, no. 2, 2020, pp. 43-54, doi:10.47087/mjm.549174.
Vancouver Noureddine B. A CLASS OF THIRD-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL CONDITION AT RESONANCE. Maltepe Journal of Mathematics. 2020;2(2):43-54.

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