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Under suitable assumptions on $h(x)$, we first prove the existence of ground state solutions by the mountain-pass theorem for $p>4$; then we verify the existence of ground state sign-changing solutions based on the method of Nehari manifold for $p>6$. 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Under suitable assumptions on $h(x)$, we first prove the existence of ground state solutions by the mountain-pass theorem for $p>4$; then we verify the existence of ground state sign-changing solutions based on the method of Nehari manifold for $p>6$. 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