The book deals with parameter dependent problems of the form
u"+*f(u)=0 on an interval with homogeneous Dirichlet or Neuman
boundary conditions. These problems have a family of solution
curves in the (u, *)-space. By examining the so-called time maps of
the problem the shape of these curves is obtained which in turn
leads to information about the number of solutions, the dimension
of their unstable manifolds (regarded as stationary solutions of
the corresponding parabolic prob- lem) as well as possible orbit
connections between them. The methods used also yield results for
the period map of certain Hamiltonian systems in the plane. The
book will be of interest to researchers working in ordinary
differential equations, partial differential equations and various
fields of applications. By virtue of the elementary nature of the
analytical tools used it can also be used as a text for
undergraduate and graduate students with a good background in the
theory of ordinary differential equations
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