On the number of positive solutions of a quasilinear elliptic problem Giovany FigueiredoMarcelo Furtado 26positive solutionsLjusternik-Schnirelmann theoryquasilinear problemspenalization method We obtain multiplicity of positive solutions for the quasilinear equation \[ {-}\varepsilon^{p} \div(a(x)|\nabla u|^{p-2} \nabla u) + u^{p-1} = f(u) \quad\mbox{in }\mathbb{R}^{N}, \quad u \in W^{1,p}(\mathbb{R}^{N}), \] where $\varepsilon > 0$ is a small parameter, $1 < p < N$, $f$ is a subcritical nonlinearity and $a$ is a positive potential such that $\inf_{\partial\Lambda}a > \inf_{\Lambda}a$ for some open bounded subset $\Lambda \subset \mathbb{R}^{N}$. We relate the number of positive solutions with the topology of the set where $a$ attains its minimum in $\Lambda$. The result is proved by using Ljusternik-Schnirelmann theory. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2832 10.1512/iumj.2006.55.2832 en Indiana Univ. Math. J. 55 (2006) 1835 - 1856 state-of-the-art mathematics http://iumj.org/access/