Infinitely many positive solutions for a nonlinear field equation with super-critical growth (Q2795900)

In the paper under review, the authors consider the following nonlinear field equation with super-critical growth: NEWLINE\[NEWLINE\begin{aligned} -\Delta u+\lambda u=Q(y)u^{(N+2)/(N-2)}, \quad u>0 \quad & \text{in } \mathbb{R}^{N+m}, \\ u(y)\to 0 \quad & \text{as } |y| \to +\infty, \end{aligned} NEWLINE\]NEWLINE where \(m \geq 1\), \(\lambda \geq 0\), and \(Q\) is a bounded positive function which satisfies some symmetry conditions. The exponent \((N+2)/(N-2)\) is super-critical in \(\mathbb{R}^{N+m}\).NEWLINENEWLINEBy constructing solutions that concentrate at a large number of \(m\)-dimensional manifolds, the authors prove the existence of infinitely many positive solutions for the considered problem.