Application of local linking to asymptotically linear wave equations with resonance
The authors provide a proof of the existence of a nontrivial time-periodic solution to the following nonlinear wave equation (WE) with asymptotically linear nonlinear term \(h(\square:=\partial^2/\partial t^2-\partial^2/\partial x^2)\): \[ \begin{cases} \square u(x,t)=h\bigl(x,t,u(x,t)\bigr), \quad & (0<x<\pi,\;t\in\mathbb{R}),\\ u(0,t)=u(\pi,t)=0\quad & (t\in\mathbb{R}),\\ u(x,t+2\pi)=u(x,t)\quad & (0<x<\pi,\;t\in\mathbb{R})\end{cases}.\tag{WE} \] This is a well written paper with interesting results.
scientific article; zbMATH DE number 5079799