Existence and the number of solutions of nonresonant semilinear equations and applications to boundary value problems

In this paper, we study the existence and the finiteness of the number of solutions to nonlinear equations and to nonresonant semilinear equations involving nonlinear perturbations of Fredholm maps of index zero. Applications are given to semilinear elliptic boundary value problems and to semilinear parabolic and hyperbolic periodic-boundary value problems.