On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems

摘要

We study a quasilinear elliptic problem $$ left{begin{array}{ll} -,{rm div}(phi(|nabla u|)nabla u) = lambda f(x,u) &quadtext{in ${rm Omega}$} u = 0 &quadtext{on $partial{rm Omega}$}end{array}right.$$ with nonhomogeneous principal part φ. Under the hypothesis f(x,t)= o(φ(t)t) at t= 0 and ∞, the existence of multiple positive solutions is proved by using the variational arguments in the Orlicz–Sobolev spaces.