TY - JOUR AU - Sreedhar, N. AU - Madhubabu, B. AU - Prasad, K.R. PY - 2023/03/08 Y2 - 2024/03/29 TI - Existence Results for Differential Equations of Fourth Order with Non-Homogeneous Boundary Conditions JF - Contemporary Mathematics JA - Contemp. Math. VL - 4 IS - 1 SE - Research Article DO - 10.37256/cm.4120232206 UR - https://ojs.wiserpub.com/index.php/CM/article/view/2206 SP - 118-131 AB - <p>The objective of this paper is to investigate the existence and uniqueness of solutions to fourth order differential equations<br /><em>                                                           v</em><sup>(4)</sup> (<em>x</em>) +<em> f</em> (<em>x</em>, <em>v</em>(<em>x</em>)) = 0, <em>x</em>∈[a,b],<br />satisfying the three-point non-homogeneous conditions<br /><em>                                                 v</em>(a) = 0, <em>v′</em>(a) = 0, <em>v′′</em>(a) = 0, <em>v′</em>(b) −<em>α v′</em>(<em>ζ</em> ) =<em> μ</em>,<br />where 0 ≤ a &lt; ζ &lt; b, the constants <em>α</em>, <em>μ</em> are real numbers and <em>f</em> : [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.</p> ER -