In this paper, we study the critical points of stable solutions for the following p-laplacian equation \(\begin{aligned} {\left\{ \begin{array}{ll} -\textrm{div}\big (|\nabla u|^{p-2}\nabla u\big )=f(u)& \textrm{in}\ \Omega ,\\ u>0& \textrm{in}\ \Omega ,\\ u=0& \textrm{on}\ \partial \Omega , \end{array}\right. } \end{aligned}\) where \(p>2\) , \(f\in C^1([0,+\infty ))\) satisfies \(f(t)>0\) for \(t>0\) , and \(\Omega \subset \mathbb {R}^2\) is a smooth bounded domain with non-negative curvature of the boundary. Via a suitable approximation argument, we prove that a stable solution u admits only internal absolute maxima and possibly saddle points with zero index as its critical point. Moreover, \(\textrm{Argmax}(u)\) is a point or a segment.
