Solvability of Higher Order Iterative System with Non-Homogeneous Integral Boundary Conditions

Authors

DOI:

https://doi.org/10.37256/cm.3220221300

Keywords:

differential equation, iterative system, integral boundary conditions, eigenvalues, kernel, positive solution

Abstract

The aim of this paper is to establish the existence of positive solutions by determining the eigenvalue intervals of the parameters μ1, μ2, ..., μm for the iterative system of nonlinear differential equations of order p

 

              wi(p) (x) + μi ai (x) fi (wi+1 (x) ) = 0, 1 ≤ i ≤ m, x∈ [0,1], 

 

                             wm+1 (x) = w1 (x), x ∈ [0,1],

 

satisfying non-homogeneous integral boundary conditions

 

                          wi (0) = 0, wi' (0) = 0, ..., wi(p-2) (0) = 0,

 

                       wi(r) - ηi 01gi(τ)wi(r)(τ)dτ = λi, 1 ≤ i ≤ m,

 

where r ∈ {1, 2, ..., p−2} but fixed, p ≥ 3 and ηi, λi ∈ (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.

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Published

2022-04-21

How to Cite

1.
Namburi S, Namana K, Rajendra Prasad Kapula. Solvability of Higher Order Iterative System with Non-Homogeneous Integral Boundary Conditions. Contemporary Mathematics [Internet]. 2022 Apr. 21 [cited 2022 Jun. 28];3(2). Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1300