Remarks on time map for quasilinear equations

We present two different generalizations of R. Schaafʹs (1990) [18] time map formula to quasilinear equations, including the case of p-Laplacian. We give conditions for monotonicity and for convexity of the time map, which imply uniqueness or multiplicity results for the corresponding Dirichlet boundary value problem. Our time map formulas can be also used for effective computations of the global solution curves.