Positive Solutions for Third Order Three-Point Boundary Value Problems with $p$-Laplacian (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, the existence of positive solutions of the followingthird-order three-point boundary value problem with $p$-Laplacian $$\begin{cases}(\phi_p(u''(t)))'+f(t,u(t))=0, \ t\in(0,1), \\ u(0)=\alpha u(\eta),\ u(1)=\alpha u(\eta), \ u''(0)=0,  \end{cases}$$is studied, where $\phi_p(s) = |s|^{p−2} s,$ $p > 1.$ By using the fixed point indexmethod, we establish sufficient conditions for the existence of at least one orat least two positive solutions for the above boundary value problem. Themain result is demonstrated by providing an example as an application.
Keywords: Positive solution; three-point boundary value problem; fixed point index; $p$-Laplacian operator.