Existence and multiplicity results for equations with nearly critical growth (Q719202)

The paper under review deals with the study of positive solutions of the nonlinear elliptic equation \(-\Delta u=K(x)u^{p-\varepsilon}\) in \({\mathbb R}^n\) (\(n\geq 3\)), where \(\varepsilon >0\), \(p=(n+2)/(n-2)\), and \(K\) is a positive and bounded potential with bounded gradient. The main result in this paper establishes an existence and multiplicity property for single peaked solutions. The proof combines the Lyapunov-Schmidt reduction method with related elliptic estimates.