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We prove that a variational quasilinear elliptic equation admits a positiveweak solution on $\mathbb R^n$. Our results extend to a wider class of equationssome known results about semilinear and quasilinear problems: all thecoefficients involved (also the ones in the principal part) depend both on thevariable $x$ and on the unknown function $u$; moreover, they are nothomogeneous with respect to $u$.

Positive entire solutions of quasilinear elliptic problems via nonsmooth critical point theory