Let \(B_1\) denote the unit ball centered at the origin in \({\mathbb {R}}^N\) with \(N = 2 n \ge 4\) and \(p>2\) . In this work we are interested in finding positive classical nonradial solutions u of \(\begin{aligned} \left\{ \begin{array}{ll} -\Delta u(x) + \frac{ \beta x \cdot \nabla u}{|x|^{2+\delta }} = u^{p-1} & \text{ in } B_1 \backslash \{0\}, \\ u=0 & \text{ on } \partial B_1. \\ \end{array}\right. \end{aligned}\) where \( \beta >0\) and \( \delta >0\) . Note that for \( \delta >0\) the gradient term is supercritical, in the sense that the term \( \beta (x \cdot \nabla u)/|x|^{2+\delta } \) exhibits a stronger singularity at the origin than in the critical case \(\delta = 0\) .
