The Existence Of Nonoscillatory Solutions For The Second Order Nonlinear Neutral Dynamic Equations With Positive And Negative Terms

In this paper, we consider the existence of nonoscillatory solutions for the sec-ond order nonlinear dynamic equation with positive and negative terms and itscorresponding with forced termsAlso, consider the neutral equation with oscillatory coefficients:We assume that,(H₂)(?)(t)=∞,(?)(t)is strictly increasing,and ((?)^-1(t))^â–³is bounded;(H₃)f_i∈C_rd(T×R,R)and uf_i(t,u)>0 for u≠0,where i=1,2ï¼›(H₄) A_i(t)∈C_rd(T,R)is allowed changing signs all the time (i.e.oscillatoryaround zero).By define mappings, using the Banach contraction mapping principle andKransnoselskii's fixed theorem, we obtain the existence of nonoscillatory solutionsfor the above equations.