Existence and multiplicity results for infinitely many solutions for Kirchhoff-type problems in \(\mathbb{R}^N\) (Q2922233)

The existence of solutions of Kirchhoff type problems \(-(a + b \int_{\mathbb{R}^{N}} | \nabla u | ^{2}\, dx ) \Delta u +u=f(x,u)\), \(u \in H^{1}(\mathbb{R}^{N})\) is investigated. One gives sufficient conditions in order that the problem has at least one solution or infinitely many solutions. But we have to remark that the paper contains a series of missprints which can create a discomfort to the reader: e.g., the Palais-Smale (PS) compactness condition formulation (p. 1832) is incomplete.