Henon equation with nolinearities involving Sobolev critical growth in H^1
DOI:
https://doi.org/10.58997/ejde.2021.20Keywords:
Henon type equation; critical Sobolev growth; resonance; noncompact variational problemAbstract
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.
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