On the topological dimension of the solution set of a class of nonlocal elliptic problems. (English) Zbl 1308.35030

Faraci, Francesca; Iannizzotto, Antonio

Topol. Methods Nonlinear Anal. 42, No. 1, 1-8 (2013).

Summary: 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.

MSC:

35B34	Resonance in context of PDEs
54F45	Dimension theory in general topology
35J25	Boundary value problems for second-order elliptic equations
35J61	Semilinear elliptic equations

Keywords:

nonlocal boundary value problems; equation of resonant type