TY - JOUR
AU - R. Ravi Sankar,
AU - N. Sreedhar,
AU - K. R. Prasad,
PY - 2021/05/08
Y2 - 2024/05/31
TI - Existence Results for Fourth Order Non-Homogeneous Three-Point Boundary Value Problems
JF - Contemporary Mathematics
JA - Contemp. Math.
VL - 2
IS - 2
SE - Research Article
DO - 10.37256/cm.222021780
UR - https://ojs.wiserpub.com/index.php/CM/article/view/780
SP - 162-172
AB - <p>The present paper focuses on establishing the existence and uniqueness of solutions to the nonlinear differential equations of order four y<sup>(4)</sup>(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.</p>
ER -