Existence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems

Authors

  • R. Ravi Sankar Department of Mathematics, Government Degree College Tekkali, Srikakulam, India
  • N. Sreedhar Department of Mathematics, Institute of Science GITAM, Visakhapatnam, India https://orcid.org/0000-0002-3916-3689
  • K. R. Prasad Department of Applied Mathematics, College of Science and Technology Andhra University, Visakhapatnam, India

DOI:

https://doi.org/10.37256/cm.222021780

Keywords:

nonlinear boundary value problem, non-homogeneous boundary conditions, kernel, existence and uniqueness of solution, fixed point theorem

Abstract

The present paper focuses on establishing the existence and uniqueness of solutions to the nonlinear differential equations of order four y(4)(t) + g(t, y(t)) = 0, t ∈ [a, b], together with the non-homogeneous three-point boundary conditions y(a) = 0, y′(a) = 0, y′′(a) = 0, y(b) − αy(ξ ) = λ, where 0 ≤ a < b, ξ ∈ (a, b), α, λ are real numbers and the function g: [a, b] × R→R is a continuous with g(t, 0) ≠ 0. With the aid of an estimate on the integral of kernel, the existence results to the problem are proved by employing fixed point theorem due to Banach.

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Published

2021-05-08

How to Cite

1.
R. Ravi Sankar, N. Sreedhar, K. R. Prasad. Existence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems. Contemp. Math. [Internet]. 2021 May 8 [cited 2023 Jan. 31];2(2):162-7. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/780