The Existence Of Solutions Of Boundary Value Problems For Differential Equations On Infinite Interval

Modern science and technology is in high speed development stage. Differential equation boundary value problem is applied to more and more disciplines, such as rheology, fluid flow, electricity network, viscoelasticity, chemical physics, electronics, biology, and control theory, etc. Scholars, in the process of practical researching the differential equation boundary value, found that it could be roughly divided into the boundary value problems of differential equation on the infinite interval and the boundary value problems of differential equation on the finite interval based on the different scope of variables; According to its corresponding homogeneous equation having a nontrivial solution or not, it is generally classified into resonant and non-resonant differential equation boundary value problem. The research of resonant differential equations on the infinite interval has been always a difficulty. Although it has made some research achievements, there are still many problems unsolved. In this thesis, the author does a further research the differential equations at resonance on the infinite interval and gives the existence theory of the solutions for two kinds of differential equations boundary value problem. The main contents of the research are as follows:1)A research for a kind of differential equations boundary value problem at resonance on half infinite interval with p-Laplacian operator is studied in Chapter Two. By constructing proper Banach spaces,defining the appropriate operators, the author uses the extension of Mawhin’s continuous theorem, and obtains the existence theorem of the solution of equations at resonance.2)A study for second order differential equation boundary value problem at resonance on half infinite interval is researched in Chapter Three. By building the appropriate Banach spaces, defining the appropriate operators, the author uses the Leggett-Williams norm-type theorem, and concludes the existence theorem of positive solution for the boundary value problem at resonance.