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

#### Abstract

We prove that a variational quasilinear elliptic equation admits a positive

weak solution on $\mathbb R^n$. Our results extend to a wider class of equations

some known results about semilinear and quasilinear problems: all the

coefficients involved (also the ones in the principal part) depend both on the

variable $x$ and on the unknown function $u$; moreover, they are not

homogeneous with respect to $u$.

weak solution on $\mathbb R^n$. Our results extend to a wider class of equations

some known results about semilinear and quasilinear problems: all the

coefficients involved (also the ones in the principal part) depend both on the

variable $x$ and on the unknown function $u$; moreover, they are not

homogeneous with respect to $u$.

#### Keywords

variational quasilinear elliptic equation; positive weak solutions; nonsmooth critical point theory

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