creative_2022_31_1_101_108This paper establishes the existence of positive solutions for 
order differential equations with 
-Laplacian operator
![\[(-1)^n[\phi_{p}(v^{(3n-3)}(t))]'''=g(t,v(t)), ~~t \in [0, 1],\]](https://www.creative-mathematics.cunbm.utcluj.ro/wp-content/ql-cache/quicklatex.com-69b9b6ca75f83a05093d1a8c39f6ff63_l3.png "Rendered by QuickLaTeX.com")
satisfying the three-point boundary conditions
![\[\left. \begin{aligned} v^{(3i)}(0)=0&,~ v^{(3i+1)}(0)=0,~ v^{(3i+1)}(1)=\alpha_{ i+1}v^{(3i+1)}(\eta), \text{~for~} 0\leq i \leq n-2,\\ &[\phi_{p}(v^{(3n-3)}(t))]_{\text {at} ~ t=0}=0,~ [\phi_{p}(v^{(3n-3)}(t))]_{\text {at} ~ t=0}'= 0,\\ &~~[\phi_{p}(v^{(3n-3)}(t))]_{\text {at} ~ t=1}'=\alpha_{n}[\phi_{p}(v^{(3n-3)}(t))]_{\text {at} ~ t=\eta}', \end{aligned} \right\}\]](https://www.creative-mathematics.cunbm.utcluj.ro/wp-content/ql-cache/quicklatex.com-95be72964abe88cfb3dc247498eb779d_l3.png "Rendered by QuickLaTeX.com")
where 
,\ 
, 
is a constant for 
by an application of Guo–Krasnosel’skii fixed point theorem.
| Author(s) | Sankar, R. R., Prasad, K. R., Sreedhar, N. |
|---|
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