
   @article{article_845044, title={Existence of Positivity of the Solutions for Higher Order Three-Point Boundary Value Problems involving p-Laplacian}, journal={Advances in the Theory of Nonlinear Analysis and its Application}, volume={6}, pages={451–459}, year={2022}, DOI={10.31197/atnaa.845044}, author={Sankar, Ravi and Namburi, Sreedhar and Rajendra Prasad, Kapula}, keywords={three-point, nonlinear, boundary value problem, p-Laplacian, Green’s function, positive solution}, abstract={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’skii fixed point theorem to determine the existence of positivity of the solutions to the problem.}, number={4}, publisher={Erdal KARAPINAR}
