Existence of nonnegative solution for a boundary value problem via upper and lower method on the half-line

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-5202

Keywords:

second order, fixed point theorem, upper and lower solutions, Nagumo condition

Abstract

In this paper, we provide existence results to the following boundary value problem

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where q ∈ L1 ((0, +∞), R) and the nonlinearity f: [0, +∞ [×R×R→ R is continuous.

 

 

References

R.P. Agarwal, D. O'Regan, Infinite Interval Problems for Differential, Difference, and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001.

A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems, J. Math. Anal. Appl., 185(2) (1994), 302-320.

E. Cetin and R. P. Agarwal Existence of solutions for fourth order three-point boundary value problems on half- line, EJQTDE, 62 (2015), 1-23.

C. Corduneanu, Integral Equations and Stability of Freedback Systems, Academic Press, New York, 1973.

K. Deimling, Nonlinear Functional Analysis. Springer-Verlag, Berlin, Heidelberg, 1985.

S. Djebali and O. Saifi, Positive solution for singular phi-Laplacian BVPs on the positive half-line, EJQTDE, 56 (2009), 24pp.

S. Djebali and O. Saifi, Upper and lower solution method for singular phiLaplacian BVPs with derivative depending nonlinearity on [0;+1), Commun. Appl. Anal., 14(4) (2010), 463{480.

Z. Du, W. Liu and X. Lin, Multiple solutions to a three-point boundary value problem for higher-order ordinary differential equations, J. Math. Anal. Appl., 335(2) (2007), 1207-1218.

Y. Guo, C. Yu and J. Wang, Existence of three positive solutions for m-point boundary value problems on infinite intervals, Nonlinear Anal., 71(3-4) (2009), 717-722.

H. Lian, P. Wang and W. Ge, Unbounded upper and lower solutions method for Sturm-Liouville boundary value problem on infinite intervals, Nonlinear Anal., 70(7) (2009), 2627{2633.

H. Lian, J. Zha and R. P. Agarwal, upper and lower solution method for nth order BVPs on an infinite interval, Bound. Value Probl., 1 (2014), 1-17.

K. Schmitt, A nonlinear boundary value problem, J. Diff. Equs, 7 (1970), 527-537.

X. Su and S. Zhang, Unbounded solutions to a boundary value problem of fractional order on the half-line, Computers and mathematics with applications, 61 (2011), 1079-1087.

B. Yan and Y. Liu, Unbounded solutions of the singular boundary value problems for second order differential equations on the half line, Appl. Math. Comput., 147 (3)(2004), 629{644.

B. Yan, R.P. Agarwal and D. O'Regan, Positive solutions for second order singular boundary value problems with derivative dependence on infinite intervals, Acta Appl. Math., 103 (1)(2008), 19-57.

Y. Zhao, H. Chen and C. Xu Existence of multiple solutions for three-point boundary value problems on infinite intervals in Banach spaces, Elect. J. Diff. Eqs., 44 (2012), 1{11.

Published

2024-05-15

How to Cite

[1]
Z. Youcef, K. Bachouche, and T. Moussaoui, “Existence of nonnegative solution for a boundary value problem via upper and lower method on the half-line”, Proyecciones (Antofagasta, On line), vol. 43, no. 3, pp. 665-682, May 2024.

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Artículos