This paper studies the Cauchy problem of semi-linear σ-evolution equations with structural damping,and the(Lm ∩ L2)-L2 and L2-L2 estimates of the solutions of the corresponding linear problems are established by Fourier analysis.Employing the global iterative method and assuming small initial data,when the nonlinear term exponent p and the spatial dimension n meet certain conditions,the global existence and uniqueness of the solutions are proved and the decay estimates are obtained.
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