Existence and multiplicity of positive unbounded solutions for singular BVPs with the φ-Laplacian operator on the half line

Authors

  • Chahira Attia University of Boumerdes
  • Salima Mechrouk University of Boumerdes.
  • Ouiza Saifi Algiers University 3.

DOI:

https://doi.org/10.22199/issn.0717-6279-4658

Keywords:

cones, second order, unbounded solution, singular problem, fixed point theory, positive solution, BVPs

Abstract

We provide in this work sufficient conditions for existence and multiplicity of positive unbounded solutions for a class of singular second-order boundary value problem associated with a φ-Laplacian operator and posed on the half-line. The proofs are based on a theorem of cone expansion and compression in a Banach space.

Author Biographies

Chahira Attia, University of Boumerdes

Dynamic of Engines and Vibroacoustic Laboratory, Faculty of Sciences.

Salima Mechrouk, University of Boumerdes.

Faculty of Sciences.

Ouiza Saifi, Algiers University 3.

Departement of Economics, Faculty of Economic and Management Sciences.

References

R. P. Agarwal and D. O’Regan, “Second-Order Boundary Value Problems of Singular Type”, Journal of mathematical analysis and applications, vol. 226, no. 2, pp. 414–430, 1998. https://doi.org/10.1006/jmaa.1998.6088

R. P. Agarwal and D. O’Regan, Infinite interval problems for differential, difference and integral equations. Dordrecht: Kluwer Academic Publishers, 2001.

C. Corduneanu, Integral equations and stability of feedback systems. New York: Academic Press, 1973.

S. Djebali and O. Saifi, “Positive solutions for singular ϕ−Laplacian BVPs on the positive half-line”, Electronic journal of qualitative theory of differential equations, no. 56, pp. 1–24, 2009. https://doi.org/10.14232/ejqtde.2009.1.56

D. Guo and V. Lakshmikantham, Nonlinear problems in abstract cones. San Diego: Academic Press, 1988.

P. Kang and Z. Wei, “Multiple solutions of second-order three-point singular boundary value problems on the half-line”, Applied mathematics and computation, vol. 203, no. 2, pp. 523–535, 2008. https://doi.org/10.1016/j.amc.2008.04.057

S. Liang and J. Zhang, “The existence of countably many positive solutions for nonlinear singular m-point boundary value problems on the half-line”, Journal of computational and applied mathematics, vol. 222, no. 2, pp. 229–243, 2008. https://doi.org/10.1016/j.cam.2007.10.062

S. Liang and J. Zhang, “The existence of countably many positive solutions for one-dimensional p-Laplacian with infinitely many singularities on the half-line”, Applied mathematics and computation, vol. 201, no. 1-2, pp. 210–220, 2008. https://doi.org/10.1016/j.amc.2007.12.016

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, vol. 205, no. 2, pp. 751–763, 2007. https://doi.org/10.1016/j.cam.2006.02.055

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, vol. 197, no. 2, pp. 365–386, 2006. https://doi.org/10.1016/j.cam.2005.11.010

Y. Liu, “Existence and unboundedness of positive solutions for singular boundary value problems on half-line”, Applied mathematics and computation, vol. 144, no. 2-3, pp. 543–556, 2003. https://doi.org/10.1016/s0096-3003(02)00431-9

Published

2022-01-28

How to Cite

[1]
C. . Attia, S. Mechrouk, and O. . Saifi, “Existence and multiplicity of positive unbounded solutions for singular BVPs with the φ-Laplacian operator on the half line”, Proyecciones (Antofagasta, On line), vol. 41, no. 1, pp. 1-22, Jan. 2022.

Issue

Section

Artículos