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About the existence and uniqueness of solutions for some second-order nonlinear BVPs

Author

Listed:
  • Yadav, Sonia
  • Singh, Sukhjit
  • Hernández-Verón, M.A.
  • Martínez, Eulalia
  • Kumar, Ajay
  • Badoni, R.P.

Abstract

The significance of our work is to solve some second-order nonlinear boundary value problems. To do this, we take into account the equivalence of the problems considered with certain integral equations, we will obtain a fixed-point-type result for these integral equations. This result provides us the existence and uniqueness of solutions for the second-order nonlinear boundary value problems considered. As a novelty, we will use for this fixed-point-type result a family of third order iterative processes to approximate the solution, instead of the usually considered method of Successive Approximations of linear convergence.

Suggested Citation

  • Yadav, Sonia & Singh, Sukhjit & Hernández-Verón, M.A. & Martínez, Eulalia & Kumar, Ajay & Badoni, R.P., 2023. "About the existence and uniqueness of solutions for some second-order nonlinear BVPs," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003879
    DOI: 10.1016/j.amc.2023.128218
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