Nonlinear Integral Equations And Nonlinear Ordinary Differential Equation Boundary Value Problem,

With the development of science and technology, an overgrowing interest in various nonlinear problems has been aroused. Thus nonlinear analysis, aimed at studying nonlinear problems, is of profound theoretical significance and wide application. This explains the reason why it has become among the most important direction in modern mathematics.Boundary value problems for nonlinear differential equation have found many applications in science and engineering. Covering two-point boundary value problems, multipoint value problems as special cases, integral boundary problems for ordinary differential equations have their roots in applied sciences such as physics and chemistry.In this paper, we use the method of supersolution and subsolution, fixed point index theory, and fixed point theorems of expansion and compression type on a cone to study the existence, uniqueness and multiplicity of positive solutions for some nonlin-ear problems, including integral boundary value problems, systems of nonlinear integral equations, and systems of two-point boundary value problems for 2nth nonlinear ordi-nary differential equations.The thesis is divided into four chapters.In Chapter One, by using the method of supersolution and subsolution, we study the existence and uniqueness of positive solutions for the Sturm-Liouville integral boundary value problem Here p∈C1([0,1],(0,+∞)),q∈C([0,1],R+),αi≥0;f(x,u)=∑i=1nbi(x)uai,where bi(x)(i=1,2,…n) is nonnegative and continuous,00. Our results extend and improve some related works in the literature.