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The interesting features in our proof are that neither asymptotic behavior of u at infinity nor symmetric property of u are required. Moreover, when $p=\\frac{N+4}{N-4}$, we can also obtain nonexistence of nontrivial nonnegative classical radial solutions of (0.2). Nonexistence of nontrivial nonnegative classical solutions without symmetry property of (0.2) with $p=\\frac{N+4}{N-4}$ is still open. 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