Nontrivial solutions of boundary value problems for second order functional differential equations

In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point index on affine cones. This approach is fairly general and covers a class of nonlocal boundary value problems for functional differential equations. Some examples are given in order to illustrate our theoretical results.Comment: 19 pages, revised versio

Periodic perturbations of constrained motion problems on a class of implicitly defined manifolds

We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios of a nontrivial unperturbed force field and of perturbation of the zero field. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions. We apply our construction to a class of second order Differential-Algebraic Equations.Comment: 15 pages, 2 figures, to appear in Communications in Contemporary Mathematics. arXiv admin note: substantial text overlap with arXiv:1102.156