This book is devoted to the study of positive solutions to indefinite problems. The monograph
intelligibly provides an extensive overview of topological methods and introduces new ideas and
results. Sticking to the one-dimensional setting the author shows that compelling and
substantial research can be obtained and presented in a penetrable way. In particular the book
focuses on second order nonlinear differential equations. It analyzes the Dirichlet Neumann
and periodic boundary value problems associated with the equation and provides existence
nonexistence and multiplicity results for positive solutions. The author proposes a new
approach based on topological degree theory that allows him to answer some open questions and
solve a conjecture about the dependence of the number of positive solutions on the nodal
behaviour of the nonlinear term of the equation. The new technique developed in the book gives
as a byproduct infinitely many subharmonic solutions and globally defined positive solutions
with chaotic behaviour. Furthermore some future directions for research open questions and
interesting unexplored topics of investigation are proposed.
