14 citations · 87 across the 38 of their papers we have counts for
5 papers · 1 filter
Positive eigenvectors and simple nonlinear maps
Marta Calanchi, Carlos Tomei
For linear operators and nonlinear maps , we describe classes of simple maps , between Banach and Hilbert spaces, for which no point has more tha…
The geometry of the critical set of nonlinear periodic Sturm-Liouville operators
Dan Burghelea, Nicolau C. Saldanha, Carlos Tomei
We study the critical set C of the nonlinear differential operator F(u) = -u" + f(u) defined on a Sobolev space of periodic functions H^p(S^1), p >= 1. Let R^2_{xy} \subset R^3 be…
The topology of critical sets of some ordinary differential operators
Nicolau C. Saldanha, Carlos Tomei
We survey recent work of Burghelea, Malta and both authors on the topology of critical sets of nonlinear ordinary differential operators. For a generic nonlinearity , the critic…
Results on infinite dimensional topology and applications to the structure of the critical set of nonlinear Sturm-Liouville operators
Dan Burghelea, Nicolau C. Saldanha, Carlos Tomei
We consider the nonlinear Sturm-Liouville differential operator for , a Sobolev space of functions satisfying Dirichlet boundary condition…
Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type
H. Bueno, C. Tomei
The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of functions that satisfy the Diric…