@article{Namburi_Namana_Rajendra Prasad Kapula_2022, title={Solvability of Higher Order Iterative System with Non-Homogeneous Integral Boundary Conditions}, volume={3}, url={https://ojs.wiserpub.com/index.php/CM/article/view/1300}, DOI={10.37256/cm.3220221300}, abstractNote={<p>The aim of this paper is to establish the existence of positive solutions by determining the eigenvalue intervals of the parameters <em>μ<sub>1</sub>, μ<sub>2</sub>, ..., μ<sub>m</sub></em> for the iterative system of nonlinear differential equations of order<em> p</em></p> <p> </p> <p><em>              w<sub>i</sub></em><sup>(<em>p</em>) </sup><sub><sup>(</sup></sub><em>x</em><sub><sup>) + <em>μ</em></sup><em>i </em></sub><em>a<sub>i </sub></em>(<em>x</em>) <em>f<sub>i </sub></em>(<em>w<sub>i</sub></em><sub>+1 </sub>(<em>x</em>) ) = 0, 1 ≤ <em>i ≤ m, x∈ </em>[0,1], </p> <p> </p> <p><em>                             w<sub>m</sub></em><sub>+1 </sub>(<em>x</em>) = <em>w</em><sub>1 </sub>(<em>x</em>), <em>x ∈ </em>[0,1],</p> <p> </p> <p>satisfying non-homogeneous integral boundary conditions</p> <p> </p> <p><em>                          w<sub>i </sub></em>(0) = 0, <em>w<sub>i</sub>’ </em>(0) = 0, ...,<em> w<sub>i</sub><sup>(p-2) </sup></em>(0) = 0,</p> <p> </p> <p><em>                       w<sub>i</sub></em><sup>(<em>r</em>) </sup>- <em>η<sub>i </sub>∫</em><sub>0</sub><sup>1</sup><em>g<sub>i</sub></em>(<em>τ</em>)<em>w<sub>i</sub></em><sup>(<em>r</em>)</sup>(<em>τ</em>)<em>dτ = λ<sub>i</sub></em>, 1 ≤ <em>i ≤ m,</em></p> <p> </p> <p>where <em>r</em> ∈ {1, 2, ..., <em>p</em>−2} but fixed, <em>p</em> ≥ 3 and <em>η<sub>i</sub></em>, <em>λ<sub>i</sub></em> ∈ (0, ∞) are parameters. The fundamental tool in this paper is an application of the Guo-Krasnosel’skii fixed point theorem to establish the existence of positive solutions of the problem for operators on a cone in a Banach space. Here the kernels play a fundamental role in defining an appropriate operator on a suitable cone.</p>}, number={2}, journal={Contemporary Mathematics}, author={Namburi, Sreedhar and Namana, Kanakayya and Rajendra Prasad Kapula}, year={2022}, month={Apr.} }