Existence of nonnegative solutions for quasilinear elliptic equations with indefinite critical nonlinearities

摘要

We study the quasilinear elliptic equation -div(φ(|?u|)?u)= a(x)f(u)+b(x)g(u)inΩ with Dirichlet boundary condition u=0 on ?Ω, where Ω is a bounded domain in RN, a(x), b(x) are sign-changing continuous functions, and g(u) has critical growth at infinity with respect to the principal part φ. A nonnegative, nontrivial solution is given under appropriate growth conditions on f(u),g(u) at 0 and ∞.