SOME TOPOLOGICAL FIXED POINT THEOREMS FOR
NONLINEAR PROBLEMS IN ORDERED BANACH SPACES
El Khannoussi Mohammed Said1, Abderrahim Zertiti2
1,2 University Abdelmalek Essaadi
Faculty of Sciences, Department of Mathematics
BP 2121, Tetouan, MOROCCO

Abstract

We study non-linear operators which leave a cone invariant in ordered Banach spaces. We give new conditions on their derivatives which yield the existence of at least one positive fixed point.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 5
Year: 2023

DOI: 10.12732/ijam.v36i5.7

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18 (1976), 620-709.
  2. [2] M.S. El Khannoussi and A. Zertiti, Fixed points theorems in the study of positive solutions for systems of equations in ordered Banach spaces. International Journal of Applied Mahematics, 28, No 3 (2015), 291-306; doi:10.12732/ijam.v28i3.8.
  3. [3] M.S. El Khannoussi and A. Zertiti, Some variants of the contraction mapping principle for comparable elements. International Journal of Applied Mahematics, 34, No 4 (2021), 633-646; 10.12732/ijam.v34i4.3.
  4. [4] M.S. El Khannoussi and A. Zertiti, Topological methods in the study of positive solutions for operator equations in ordered Banach spaces. Electronic Journal of Differential Equations, No 171 (2016), 1-13.
  5. [5] M.S. El Khannoussi and A. Zertiti, Bounds for the spectral radius of positive operators, Electronic Journal of Differential Equations, No 29 (2022), 1-7.
  6. [6] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York (1988).
  7. [7] M.A. Krasnosel’skii, Positive Solutions of Operator Equations, Noordhoff, Groningen (1964).
  8. [8] M. A. Krasnosel’skii, Yu. V. Pokornyi, Non-zero solutions of equations with strong nonlinearities, Translated from: Matematicheskie Zametki, No 5 (1969), 253-260.
  9. [9] M. El-Shahed, Positive solutions for boundary value problems of nonlinear fractional differential equation, Abstract and Applied Analysis (2007), 1-8.