Existence of entire solutions for a class of quasilinear elliptic equations

摘要

The paper deals with the existence of entire solutions for a quasilinear equation (E)_λ in ?~N, depending on a real parameter λ, which involves a general elliptic operator in divergence form A and two main nonlinearities. The competing nonlinear terms combine each other, being the first subcritical and the latter supercritical. We prove the existence of a critical value λ* > 0 with the property that (E)_λ admits nontrivial non-negative entire solutions if and only if λ ≥ λ*. Furthermore, when λ > ?λ ≥ λ~*, the existence of a second independent nontrivial non-negative entire solution of (E)_λ is proved under a further natural assumption on A.