Multiple Solutions Of Nonlinear Boundary Value Problems With Integral Boundary Conditions On Time Scales

Ⅱn this paper, we consider the existence of positive solutions of boundary value problems with integral boundary conditions on time scales. Also, Our results of this paper are completely new.A brief description of the organization of the thesis is as follows.The first chapter describes the research backgroundand significance. The second chapter introduces some concepts, definitions and theorems.In chapter3, we consider the following third-order boundary value problems with integral boundary conditions on time scale T: where, an interval [0,1]T:=[0,1]∩T,0and1are points in T.Φp(u) is p-Laplacian operator; i.e.,Φp(u)=|u|p-2u, for p>1, with (Φp)-1=Φq, and1/p+1/q=1.By applying a generalization of the Leggett-Williams fixed point theorem, we estab-lish the existence of at least three positive solutions.In chapter4, we consider the following third-order boundary value problems with integral boundary conditions on time scale T: where, an interval[0,1]t:=[0,1]∩T,0and1are points in T, a, b, c, d>0, with ρ:=ad+ac+bc.φ:R�'R is an increasing and positive homeomorphism with φ(0)=0.By applying a generalization of the Leggett-Williams fixed point theorem, we estab-lish the existence of at least three positive solutions.