        TY  - JOUR
T1  - Existence of Positivity of the Solutions for Higher Order Three-Point Boundary Value Problems involving p-Laplacian
AU  - Namburi, Sreedhar
AU  - Sankar, Ravi
AU  - Rajendra Prasad, Kapula
PY  - 2022
DA  - December
DO  - 10.31197/atnaa.845044
JF  - Advances in the Theory of Nonlinear Analysis and its Application
JO  - ATNAA
PB  - Erdal KARAPINAR
WT  - DergiPark
SN  - 2587-2648
SP  - 451
EP  - 459
VL  - 6
IS  - 4
LA  - en
AB  - The present study focusses on  the  existence of  positivity of the  solutions to the higher order  three-point boundary value problems involving  $p$-Laplacian$$[\phi_{p}(x^{(m)}(t))]^{(n)}=g(t,x(t)),~~t \in [0, 1],$$$$\begin{aligned}x^{(i)}(0)=0, &amp;\text{~for~}  0\leq i\leq m-2,\\x^{(m-2)}(1)&amp;-\alpha x^{(m-2)}(\xi)=0,\\[\phi_{p}(x^{(m)}(t))]^{(j)}_{\text {at} ~ t=0}&amp;=0, \text{~for~} 0\leq j\leq n-2,\\[\phi_{p}(x^{(m)}(t))]^{(n-2)}_{\text {at} ~ t=1}&amp;-\alpha[\phi_{p}(x^{(m)}(t))]^{(n-2)}_{\text {at} ~ t=\xi}=0,\end{aligned} $$ where $m,n\geq 3$, $\xi\in(0,1)$, $\alpha\in (0,\frac{1}{\xi})$  is a parameter.The approach used by the application of Guo--Krasnosel&#039;skii fixed point  theorem to determine the existence of positivity of the  solutions to the problem.
KW  - three-point
KW  - nonlinear
KW  - boundary value problem
KW  - p-Laplacian
KW  - Green&#039;s function
KW  - positive solution
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UR  - https://doi.org/10.31197/atnaa.845044
L1  - https://dergipark.org.tr/en/download/article-file/1462317
ER  -