Manassés X. de Souza

Multiplicity of nodal solutions for elliptic problems with critical exponential growth on $$\mathbb {S}^2$$

We study the existence and multiplicity of sign-changing solutions of the semilinear elliptic equation $$ -\Delta _g u + u = f(u) \quad \text {on } \mathbb {S}^2, $$ where $$(\mathbb {S}^2,g)$$ denotes the two-dimensional unit sphere endowed with a smooth Riemannian metric, $$\Delta _g$$ is the La...