Periodic Solutions For Neutral Functional Differential Equations And On The Existence Of Solutions To Gradient Operator Equations

By applying Mawhin's continuation theorem of coincidence degree, this thesis is mainly concerned with the existence of periodic solutions for second order neutral functional differential equations. Meanwhile, the problem of solutions to second order system and a type of gradient operators equations in Hilbert space are studied by means of critical point theory. We abtain some useful results.Chapter 1 devotes to the existence of periodic solutions for second order neutral Rayleigh equation and neutral Duffing equation with complex deviating argument. The types of the equations and the approaches to estimate a priori bounds are different from those used in previous literatures.In Chapter 2, an existence theorem is obtained for periodic solutions of non-autonomous second order systems with even-typed potentials. We also investigate solutions of linear bounded positive self-conjugation operators equations in Hilbert Space by variation methods. Our ways are comprehensive and the results are new.