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 $u$.