Positivity results to iterative system of higher order boundary value problems

Kanakayya  Namana; Sreedhar  Namburi; Rajendra Prasad  Kapula

doi:10.59400/jam1829

Positivity results to iterative system of higher order boundary value problems

Kanakayya Namana Department of Mathematics, School of Science, GITAM (Deemed to be University), Visakhapatnam 530045, India
Sreedhar Namburi Department of Mathematics, School of Science, GITAM (Deemed to be University), Visakhapatnam 530045, India
Rajendra Prasad Kapula Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam 530003, India

Article ID: 1829

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DOI: https://doi.org/10.59400/jam1829

Keywords: iterative system; non-homogenous conditions; positivity results; kernel

Abstract

The present research explores the existence of positive solutions for the iterative system of higher-order differential equations with integral boundary conditions that include a non-homogeneous term. To address the boundary value problem, the solution is expressed as a solution of an equivalent integral equation involving kernels. Subsequently, bounds for these kernels are determined to facilitate further analysis. The primary tool employed in this study is the Guo-Krasnosel’skii fixed-point theorem, which is utilized to establish the existence of positive solutions within a cone of a Banach space. This approach enables a rigorous exploration of the existence of at least one positive solution and provides insights into the behavior of the differential equation under the given boundary conditions.

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Published

2024-12-09

How to Cite

Namana, K., Namburi, S., & Kapula, R. P. (2024). Positivity results to iterative system of higher order boundary value problems. Journal of AppliedMath, 2(5), 1829. https://doi.org/10.59400/jam1829

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