Positive Solutions Of Second-order Singular Boundary Value Problem(s) On Time Scales

In this paper, using the semi-order method on cones of Banach space, Lebesgue dominated convergence theorem and Fixed point index theorem, we establish the existence result for positive solution of singular nonlinear dynamic equation with parameter and the existence result for positive solution of singular nonlinear dynamic equations.The first chapter presents the background of the theory of measure chains and its development.In the second chapter, the following second-order nonlinear boundary problem with parameterλare discussed. We will establish an existence criterion for positive solution of the problem. The main tools are the fixed point index theorem and Krasnolselkii's fixed point theorem. In this article, the nonlinear term f : [0, T]_T→R~+ is continuous and can be singular at t = 0, T, and p(t) in [0, T]_T can have a finite number of singular points and can be negative, and may tend to negative infinity.In the third chapter, we will discuss the following systemWe will establish an existence criterion for positive solution of the problem. The main tools are the fixed point index theorem and Krasnolselkii's fixed point theorem. The results extend the literature [30,36,37] the result has been, and in the case of differential equations is also new.