Existence Results for Differential Equations of Fourth Order with Non-Homogeneous Boundary Conditions

Authors

  • N. Sreedhar Department of Mathematics, School of Science GITAM (Deemed to be University), Visakhapatnam, 530045, India https://orcid.org/0000-0002-3916-3689
  • B. Madhubabu Department of Mathematics, School of Science GITAM (Deemed to be University), Visakhapatnam, 530045, India https://orcid.org/0000-0003-2553-5573
  • K.R. Prasad Department of Applied Mathematics, College of Science and Technology Andhra University, Visakhapatnam, 530003, India

DOI:

https://doi.org/10.37256/cm.4120232206

Keywords:

differential equation, three-point non-homogeneous conditions, kernel, existence results, fixed point theorems.

Abstract

The objective of this paper is to investigate the existence and uniqueness of solutions to fourth order differential equations
                                                           v(4) (x) + f (x, v(x)) = 0, x∈[a,b],
satisfying the three-point non-homogeneous conditions
                                                 v(a) = 0, v′(a) = 0, v′′(a) = 0, v′(b) −α v′(ζ ) = μ,
where 0 ≤ a < ζ < b, the constants α, μ are real numbers and f : [a, b] × R → R is a continuous function. The framework for establishing the existence results is based on sharper estimates on the integral of the kernel to connect with fixed point theorems of Banach and Rus.

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Published

2023-03-08

How to Cite

1.
Sreedhar N, Madhubabu B, Prasad K. Existence Results for Differential Equations of Fourth Order with Non-Homogeneous Boundary Conditions. Contemp. Math. [Internet]. 2023 Mar. 8 [cited 2024 Mar. 4];4(1):118-31. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2206