Existence of three weak solutions to fourth-order elastic beam equations in the whole space (Q2036451)

Whenever \(\lambda\) belongs to a well precise interval of parameters, described quantitatively, the author shows the existence of at least three weak solutions for the following fourth-order problem: \[u^{(\mathrm{vi})}+Au''+Bu=\lambda \alpha(x)f(u),\] for a.e. \(x\in\mathbb{R}\), being \(\lambda\) a positive parameter, \(A\geq 0\), \(B>0\), \(\alpha \in L^1(\mathbb{R})\) with \(\alpha(x)\geq 0\) for a.a. \(x\in \mathbb{R}\) and \(f:\mathbb{R} \rightarrow \mathbb{R} \) is a suitable nonnegative continuous function. To this end, a three critical point theorem is applied in a non standard setting.