SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON THE HALF-LINE

Siham Ghiatou; John R. Graef; Toufik Moussaoui

doi:10.11948/20220531

2023 Volume 13 Issue 6

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Siham Ghiatou, John R. Graef, Toufik Moussaoui. SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON THE HALF-LINE[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3158-3165. doi: 10.11948/20220531

Citation:

Siham Ghiatou, John R. Graef, Toufik Moussaoui. SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON THE HALF-LINE[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3158-3165. doi: 10.11948/20220531

SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON THE HALF-LINE

1.
Djillali Liabes University, Sidi Bel Abbes, Algeria
2.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
3.
Laboratory of Fixed Point Theory and Applications, École Normale Supérieure, Kouba, Algiers, Algeria

Author Bio: Email: siham.ghiatou@g.ens-kouba.dz(S. Ghiatou); Email: toufik.moussaoui@g.ens-kouba.dz(T. Moussaoui)
Corresponding author: Email: John-Graef@utc.edu(J. R. Graef)

Abstract

Abstract

The authors study the existence of positive extremal solutions to the differential equation
$ -u''+\lambda u=a\left(t\right)f(t, u(t)), \quad t\in I, $
subject to the boundary conditions
$ u\left(0 \right)=u\left(\infty \right)=0, $
where $ I=(0, \infty) $, $ f: \mathbb{R^{+}\times R^{+}}\rightarrow \mathbb{R^{+}} $ is continuous, $ a:I\rightarrow \mathbb{R^{+}} $, and $ \lambda >0 $ is a parameter. Their results are obtained by using the monotone iterative method and are illustrated with an example.
- Iterative methods /
- Green's function /
- fixed point /
- boundary value problems /
- positive solution /
- operators on a cone
MSC: 47J25, 34B18, 34B25, 34B40, 34B15

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References

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