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

Authors

  • Sreedhar Namburi Department of Mathematics, Institute of Science, Gandhi Institute of Technology and Management, Visakhapatnam, India https://orcid.org/0000-0002-3916-3689
  • Kanakayya Namana Department of Mathematics, Institute of Science, Gandhi Institute of Technology and Management, Visakhapatnam, India https://orcid.org/0000-0001-5195-4486
  • Rajendra Prasad Kapula Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, India https://orcid.org/0000-0001-8162-1391

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. Contemp. Math. [Internet]. 2022 Apr. 21 [cited 2024 Mar. 4];3(2). Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1300