The Random Fixed Point Theorems On Product Cone And Its Applications

In this paper, we considered the random fixed point theorems of random com-pletely continuous operator on product cone P1×P2. We have established a random fixed point index product formula. Then some corresponding random fixed point theorems of completely continuous operator on product cone had been established. In the end, we considered the existence of random positive solutions of a second-order random differential systems with Dirichlet boundary conditions.First, we have listed some fundamental knowledge on topological degree, prob-ability theory and random fixed point index.In the first chapter, we have established product formula of random fixed point index of random completely continuous mapping and then established some random fixed point theorems of random mapping on product cone. The results of this chapter, is the promotion of the relevant results of the Chengxi You, are these fixed point theorem of random oriented.In the second chapter, to be an application of theorems established in the first chapter, we considered the existence of random positive solutions for second random differential system where for every fixed ω∈EΩ, f1(ω)∈C(J×R+×R+,R+), J=[0,1], R+[0,∞), and it is sup-linear with respect to x, meanwhile f2(ω)∈C(J×R+x R+,R+), J=[0,1], R+=[0,∞), and it is sub-linear with respect to y.