The Existence And Multiplicity Of Positive Solutions For Classes Of Boundary Value Problems Of Differential Equations

In this paper, we mainly study the existence and multiplicity of positive solutions for three classes of boundary value problems of differential equations.Firstly, by using Leggett-Williams’fixed point theorem and Holder’s inequality, the existence of three positive solutions for the fourth-order impulsive differential equations with integral boundary conditions is considered. The approximate range of three solutions is given. And we give an example to apply our results.Secondly, by using a new technique for dealing with the bending term of the fourth order p-Laplacian elasticity problems, several new and more general results are obtained for the existence of at least single, twin or triple positive solutions by using Krasnosel’skii’s fixed point theorem, fixed point theorem due to Avery and Henderson and Leggett-Williams’fixed point theorem. Besides achieving new results, estimates on the norms of these solutions will also be provided. And we give an example to apply our results.Finally, we consider the bifurcation curve of positive solutions for nonlinear boundary value problems. Two types of nonlinear term, f(u)= eu+a and f(u)= eu+up, are studied. By using the time-map method, the existence of four positive solutions for the boundary value problems is obtained.