Generic multiplicity for a scalar field equation on compact surfaces
Let \((M,g)\) be a compact Riemannian surface without boundary. The authors prove generic multiplicity of solutions as in the cases when the Euler characteristic of \(M\) is nonpositive. They prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular, their result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula by \textit{C.-C. Chen} and \textit{C.-S. Lin} [Commun. Pure Appl. Math. 56, No.~12, 1667--1727 (2003; Zbl 1032.58010)]. Moreover, related results are derived for the prescribed \(Q\)-curvature equation.
scientific article; zbMATH DE number 5782198
scientific article