On the topological dimension of the solution set of a class of nonlocal elliptic problems - Faraci, Francesca; Iannizzotto, Antonio (Topological Methods in Nonlinear Analysis, 2013)
We study a Dirichlet problem for an elliptic equation of resonant type involving a general nonlocal term. Using a result of Ricceri, we prove that the solution set for such equation has a positive topological dimension, and contains a nondegenerate connected component. In particular, the solution set has the cardinality of the continuum.