Existence Of Solutions For Some Classes Of Boundary Value Problems Of Diferential Equations On The Infinite Interval

Nonlinear functional analysis is an important branch of modern analysis mathe-matics, because it can explain kinds of natural phenomenal, more and more mathe-maticians are devoting their time to it. Among them the boundary value problems onthe infinite interval arises in diferent fields of applicable mathematics and physics. Be-cause boundary value problems on the infinite interval have wide applied background,they have important value. It is at present one of the most active fields that is studiedin mathematics.The present paper employs the theories, concepts, methods such as cone!Schauderfixed point theorem!the lower and upper solutions method!Darbo fixed point the-orem!measure of noncompactness theory and so on, to investigate the existence ofsolutions for some classes of boundary value problems of diferential equations on theinfinite interval, the obtained results are either new or intrinsically generalize and im-prove the previous relevant ones under weaker conditions.The thesis is divided into four sections according to contents.Chapter1Preference, we introduce the main contents, then give the relatedconcepts and important lemma of this paper.Chapter2We consider the following second order diferential equations withinfinite points boundary value problems on the infinite interval:the existence and uniqueness of the positive solutions for the equations are proved.Finally, the results are applied to second order boundary value problems.Chapter3In this chapter, consider the following second order diferential equa- tions with integral boundary value problems on the infinite interval:lower and upper solutions method and Schauder fixed point theorem, the existence ofsolutions as well as the positive ones is obtained. Nagumo conditions play an importantrole in the nonlinear term involved in the first-order derivatives.Chapter4At the basis of the former two chapters, in this section we considerthe following second order diferential equations with multiple points boundary valueproblems in Banach spaceBy using the Darbo fixed point theorem, the solutions of the equation(4.1.1) in Banachspace are obtained, and an example is given to demonstrate the application of our mainresults.