On the existence of infinitely many solutions for a class of semilinear elliptic equations in \(\mathbb{R}^N\) (Q1284724)

Summary: We show, by variational methods, that there exists a set \({\mathcal A}\) open and dense in \(\{a\in L^\infty(\mathbb{R}^N):a\geq 0\}\) such that if \(a\in{\mathcal A}\) then the problem \(-\Delta u+ u= a(x)| u|^{p-1}u\), \(u\in H^1(\mathbb{R}^N)\), with \(p\) subcritical (or more general nonlinearities), admits infinitely many solutions.