Monotonicity of heteroclinic orbits and spectral properties of variational equations for delay differential equations (Q1975467)

From author's introduction: He studies the monotonicity of a heteroclinic orbit (whenever it exists) and the spectral property of the variational equations asssociated to the heteroclinic orbit for a class of delay-differential equations that takes the form \[ \dot x(t)= F(x(t), x(t- r)),\quad x(t)\in \mathbb{R}^N. \] The spectral properties obtained in this paper can be used to eventually prove existence and uniqueness of the heteroclinic orbits by a global continuation, and to study existence, uniqueness, and stability of square wave periodic solutions to singularly perturbed delay-differential equations arising from modeling physical and biological problems.