Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2017), 89 -- 102

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

UNBOUNDED SOLUTIONS FOR INTEGRAL BOUNDARY VALUE PROBLEM OF SECOND-ORDER ON THE HALF-LINE

Abdellatif Ghendir Aoun

Abstract. The purpose of this paper is to establish the existence of solutions for an integral boundary value problem of second-order set on the infinite interval. The arguments we have used are based upon the nonlinear alternative of Leray-Schauder type. As applications, two examples are included to show the applicability of our result.

2010 Mathematics Subject Classification: 47H10;54H25.
Keywords: Boundary value problem; unbounded solution; infinite interval; fixed point theorem; Green's function.

Full text

References

  1. R.P. Agarwal, M. Bohner and D. O'Regan, Time scale boundary value problems on infinite intervals, Journal of Computational and Applied Mathematics 141 (2002) 27-34. MR1908826. Zbl 1001.39026.

  2. R.P. Agarwal, M. Meehan and D. O'Regan, Fixed Point Theory and Applications, Cambridge Tracts in Mathematics, vol. 141, Cambridge University Press, Cambridge(2001). MR1825411. Zbl 0960.54027.

  3. S. Chen and Y. Zhang, Singular boundary value problems on a half-line, Journal of Mathematical Analysis and Applications 195 (1995), 449-468. MR1354555.

  4. P.W. Eloe, E.R. Kaufmann and C.C. Tisdell, Multiple solutions of a boundary value problem on an unbounded domain, Dyn Syst Appl 15(1) (2006), 53-63. MR194092.

  5. J. Galvis, E.M. Rojas and A.V. Sinitsyn, Existence of positive solutions of a nonlinear second-order boundary value problem with integral boundary conditions, Electronic Journal of Differential Equations, Vol. 2015 (2015), No. 236, pp. 1-7.

  6. C.G. Kim, Solvability of multi-point boundary value problems on the half-line, J. Nonlinear Sci. Appl. 5 (2012), 27-33. MR2909235.

  7. H. Lian and W. Ge, Solvability for second-order three-point boundary value problems on a half-line, Applied Mathematics Letters 19 (2006) 1000-1006. MR2246166. Zbl 1123.34307.

  8. S. Liang, J. Zhang and Z.Wang, The existence of multiple positive solutions for multi-point boundary value problems on the half-line, Journal of Computational and Applied Mathematics 228 (2009), 10-19.

  9. Y.S. Liu, Boundary value problem for second order differential equations on unbounded domain, Acta. anal. funct. Appl. 4 (2002), 211-216. MR1956716. Zbl 1038.34030.

  10. D. O'Regan, B. Yan and R.P. Agarwal, Solutions in weighted spaces of singular boundary value problems on the half-line, Journal of Computational and Applied Mathematics 205 (2007), 751-763. MR2329651. Zbl 1124.34008.

  11. Y. Tian and W. Ge, Positive solutions for multi-point boundary value problem on the half-line, J. Math. Anal. Appl. 325 (2007), 1339-1349. MR2270088. Zbl 1110.34018.

  12. J. Tariboon and T. Sittiwirattham, Positive solutions of a nonlinear three-point integral boundary value problem, Boundary Value Problems, Vol 2010, 11 pp, DOI:10.1155/2010/519210.

  13. B. Yan, Boundary Value Problems on the Half-Line with Impulses and Infinite Delay, Journal of Mathematical Analysis and Applications 259 (2001), 94-114. MR1836447. Zbl 1009.34059.

  14. B. Yan, D. O'Regan and R.P. Agarwal, Unbounded solutions for singular boundary value problems on the semi-infinite interval: Upper and lower solutions and multiplicity, Journal of Computational and Applied Mathematics 197 (2006) 365-386. MR2260412. Zbl 1116.34016.

  15. M. Zima, On Positive Solutions of Boundary Value Problems on the Half-Line, Journal of Mathematical Analysis and Applications 259 (2001), 127-136. MR1836449. Zbl 1003.34024.



Abdellatif Ghendir Aoun
Department of Mathematics,
Faculty of Exact Sciences, El-Oued University,
P.O.Box789, 39000, El Oued, Algeria.
e-mail:ghendirmaths@gmail.com


http://www.utgjiu.ro/math/sma