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
Author(s): Rajendra Prasad Kapula a , Sreedhar Namburi
b , Mahanty Rashmita
c
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)
Full Text: PDF
Abstract
In this paper, we present criteria for the existence and nonexistence of positive solutions to nth order differential equations
, 0<
< 1
fulfilling non-homogeneous three point conditions
,
where are constants and
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
References:- P. W. Eloe, Positive solutions of boundary value problems for disfocal ordinary differential equations, J. Comput. Appl. Math. 88 (1), 71–78, 1998.
- D. Guo and V. Lakshmikantham, Nonlinear problems in abstract cones, Academic Press, Orlando, 1988.
- C. P. Gupta, Existence and uniqueness results for the bending of an elastic beam equation at resonance, J. Math. Anal. Appl. 135 (1), 208–225, 1988.
- V. A. Il’in and E. I. Moiseev, Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator, Diff. Eqs. 23, 979–987, 1987.
- M. A. Krasnosel’skii, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964.
- A. G. Lakoud and L. Zenkoufi, Existence of positive solutions for a fourth order three point boundary value problem, J. Appl. Math. Comput. 50, 139–155, 2016.
- X. Lin and Z. Zhao, Iterative technique for a third order differential equation with three point nonlinear boundary value conditions, Electron. J. Qual. Theory Differ. Equ. 12, 1–10, 2016.
- Z. Liu, H. Chen and C. Liu, Positive solutions for singular third order non-homogeneous boundary value problems, J. Appl. Math. Comput. 38, 161–172, 2012.
- R. R. Sankar, N. Sreedhar and K. R. Prasad, Existence results for fourth order non-homogeneous three point boundary value problems, Contemp. Math. 2 (2), 162–172, 2021.
- Y. Sun, Positive solutions for third order three point non-homogeneous boundary value problems, Appl. Math. Lett. 22 (1), 45–51, 2009.
- Y. Sun, Q. Sun and X. Zhang, Existence and nonexistence of positive solutions for a higher order three-point boundary value problem, Abstr. Appl. Anal. 2014, 2014; Article ID: 513051.
- Y. Sun and C. Zhu, Existence of positive solutions for singular fourth order three point boundary value problems, Adv. Difference Equ. 2013, 2013; Article ID: 51.
- Y. Wei, Q. Song and Z. Bai, Existence and iterative method for some fourth order nonlinear boundary value problems, Appl. Math. Lett. 87, 101–107, 2019.