Existence and iteration of positive pseudo-symmetric solutions for a three-point second-order \(p\)-Laplacian BVP (Q2472792)

The paper deals with the solvability of the three-point boundary value problem for the second-order \(p\)-Laplacian (BVP): \[ (\phi_{p} (u'))'+q(t)f(t,u)=0 , \qquad t \in (0,1)\,, \] \[ u(0)= 0\,, \qquad u(\eta)= u(1)\,, \qquad\, \] where \(\, \phi_{p}= | u| ^{p-2}u\,, \,\,p>1\,, \, \eta \in (0,1)\) is a constant. The monotone iterative technique is applied in order to prove the existence of positive pseudo-symmetric solutions. An example of such a BVP is considered to illustrate the theory.