On nodal solutions of the Yamabe equation on products
Usually, one looks for positive solutions of the Yamabe equation. However, solutions which change signs, called \textit{nodal}, are also important. In this case, the equation takes the form \(L_g(u)=\lambda|u|^{p-2}u\), where \(L_g\) is the Yamabe operator associated to the Riemannian metric \(g\). The main result of this paper is that the Yamabe equation associated to a Riemannian product metric has at least one nodal solution. The particular case when one of the factors in the product is the circle is separately treated and it turns out that there is an infinite number of solutions, explicitly determined.
scientific article; zbMATH DE number 5610178
scientific article