Types Of Differential Equations Existence And Multiplicity,

As an important branch of modern analysis mathematics, nonlinear functionalanalysis arises quite naturally and quickly in recent years, and what's more it applied extensively in the field of physics, chemistry and information technology, more and more mathematicians are devoting their time to it. The present paper employs the cone theory, fixed point theory, topological degree theory and upper-lower solutions method and so on, to investigate the existenceof positove solutions to BVP of some kinds of nonlinear differential equations. The results obtained are either new or essentially generalize and improve the previous relevant ones under weaker conditions.The thesis is divided into three chapters according to contents.In chapter 1, we consider the the existence of solutions for n order threepointnonhomogeneouswhere 0<η<1,αη^n-1≠0,1,1≤p<∞,f:[0,1]×Rⁿâ†'R satisfied theconditions of L_p-Caratheodory.In Chapter 2, by using the Krasnosel'skii-Guo theorem on cone expansion, we study the existence of at least one positive unbounded solutions of infinite boundary value problem of a class of singular differential equation (BVP)where a, b≥0,φ,f is continuous.φmay be singular at t = 0.In Chapter 3, we established the existence of three solutions theorem for the singular p-Laplacin nonliner bondary problem by using the Leggett- Williams theoremwhere (?)(s)=|s|^p-2s,p>1,f∈C([0,1]×[0,∞)×R,[0,∞)) and h(t)∈C((0,1),[0,∞)) may be singular at t = 0,1.