The Problem Of Periodic Solutions For P-Laplacian Functional Differential Equations And The P-Laplacian Boundary Value Problem Of Ordinary Differential Equations

By applying Mawhin's continuation theorem of coincidence degree, this dissertation is mainly concerned with the existence of periodic solutions for p—Laplacian functional differential equations and the p—Laplacian boundary value problem. We obtain some new results.Chapter 1 is the foundation of this dissertation. We mainly introduce some lemmas.Chapter 2 devotes to the existence of periodic solutions for p— Laplacian equation, Lienard equation, etc. The approaches to estimate a priori bounds are different from those used in previous literatures.In Chapter 3, several p — Laplacian neutral equations are studied. By defining the linear operators A, L and using analysis techniques, some new results are obtained.In Chapter 4, we investigate the p — Laplacian m-point boundary value problem at resonance. We can easily get the L—compact of operator N .