Open AccessExistence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems
Author(s) -
R. Sankar,
N. Sreedhar,
K. Venkatesh Prasad
Publication year - 2021
Publication title -
contemporary mathematics
Language(s) - English
Resource type - Journals
eISSN - 2705-1064
pISSN - 2705-1056
DOI - 10.37256/cm.222021780
Subject(s) - mathematics , uniqueness , fixed point theorem , boundary value problem , mathematical analysis , order (exchange) , homogeneous , banach fixed point theorem , function (biology) , picard–lindelöf theorem , continuous function (set theory) , pure mathematics , combinatorics , finance , evolutionary biology , economics , biology
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.