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The talk is concerned with the existence of solutions for semilinear degenerate elliptic equations with subcritical conditions.First,we introduce weighted $p$-Sobolev spaces and discuss the properties of continuous embedding,compactness and spectrum.Then,we talk about the corresponding Sobolev inequality and Poincar\e inequality,which are important in the proof of the existence of solutions for semi-linear degenerate elliptic equations.