Low dimension anomalies and solvability in higher dimensions for some perturbed Pohozaev equation (Q2711957)

This paper deals with the ``Pokhozhaev'' equation NEWLINE\[NEWLINE\begin{cases} -\Delta u=u^{\frac{N+2}{N-2}}+p(u) & \text{in }\Omega\\ u>0 & \text{in }\Omega\\ u=0 & \text{on }\partial\Omega.\end{cases}\tag{1}NEWLINE\]NEWLINE Here \(\Omega\subset \mathbb{R}^N\), \(N\geq 3\), is a smooth bounded domain and \(p\) is subcritical, with \(p'(0)=0\). Under some additional condition on \(p\), the author presents a new solvability condition of (1). This result seems to be sharp in some sense, has been obtained in collaboration with Adinunthi.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00021].