Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow (Q820031): Difference between revisions

In the present study the authors obtain sing-changing solutions of the problem: \[ -\left(a+b\int_\Omega|\nabla u|^2\,dx\right)\Delta u=f (x,u),\quad \text{in }\Omega, \qquad u=0,\quad\text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^N\), \(a,b>0\) and \(f\) is a given function. Under suitable assumptions on the data, the authors obtain sign-changing solutions for (1). To this end, they use variational methods and invariant sets of descent flow.