supported by NSFC (11171228,10801111,10971171),the fundamental Research Funds for the Central University (2010121006),the Natural Science Foundation of Fujian Province of China (2010J05011)
We consider a random walk on Z in random environment with possible jumps {-L,···,-1,1},in the case that the environment {ωi : i∈Z} are i.i.d..W
Let P(z) and P(z) be polynomials of the same degree.We consider the equations u''= P(z)u and u''=P(z)u(z∈C) whose solutions are u(z) and u(z),r