# Article ID: MTJPAM-D-21-00059

## Title: Existence and nonexistence results for nth order non-homogeneous three point boundary value problems

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00059; Volume 5 / Issue 1 / Year 2023, Pages 34-42

Document Type: Research Paper

aDepartment of Applied Mathematics, Andhra University, Visakhapatnam, 530 003, India

bDepartment of Mathematics, GITAM (Deemed to be University), Visakhapatnam, 530 045, India

cDepartment of Applied Mathematics, Andhra University, Visakhapatnam, 530 003, India

Received: 26 September 2021, Accepted: 12 December 2022, Published: 13 January 2023

Corresponding Author: Sreedhar Namburi (Email address: sreedharnamburi13@gmail.com)

Abstract

In this paper, we present criteria for the existence and nonexistence of positive solutions to nth order differential equations $z^{(n)}(\tau)+q(\tau)f(z(\tau))=0$, 0< $\tau$ < 1

fulfilling non-homogeneous three point conditions $z(0)=z^\prime (0)=\cdot\cdot\cdot=z^{(n-2)}(0)=0, ~\gamma z^{(n-2)}(1)-\beta z^{(n-2)}(\eta)=\nu$,

where $n>2, \eta \in (0,1), \gamma>0, \beta \in (0, \frac{\gamma}{\eta})$ are constants and $\nu \in (0, \infty)$ is a parameter by an application of fixed point index theory.

Keywords: Green’s function, differential equation, non-homogeneous three point conditions, positive solution, fixed point index theory

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