Henon equation with nolinearities involving Sobolev critical growth in H^1

Abstract

In this article we study the Henon equation $$\displaylines{ -\Delta u=\lambda |x|^{\mu} u+|x|^{\alpha}|u|^{ 2_{\alpha}^*-2}u\quad\hbox{in }B_1,\cr u =0\quad\hbox{on }\partial B_1, }$$ where \(B_1\) is the ball centered at the origin of \(\mathbb{R}^N\) \((N\geq 3)\) and \(\mu\geq \alpha\geq0\). Under appropriate hypotheses on the constant \(\lambda\), we prove existence of at least one radial solution using variational methods. For more information see https://ejde.math.txstate.edu/Volumes/2021/20/abstr.html