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We concerns with the existence and stability properties of nonconstant positive steady states in one dimensional space for the S-K-T model.By Lyapunov-Schmidt method,we obtain the existence and the detailed structure of a type of small nontrivial positive steady states to the shadow system,based on the detailed structure of the steady states,we further establish the stability of the small nontrivial positive steady state for the shadow system by spectral analysis.