We prove the existence of nontrivial ground state solutions of the critical quasilinear Hénon equation $displaystyle -Delta _p u=x^{alpha _1}u^{p^{*}(alpha _1)-2}u-x^{alpha _2}u^{p^{*}(alpha _2)-2}u {rm in} mathbb {R}^{N}.$ It is a new problem in the sense that the signs of the coefficients of critical terms are opposite.
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