Elliptic variational problems with mixed nonlinearities.

In this paper, we study the existence and multiplicity results of nontrivial positive solutions to a quasilinear elliptic equation in RN, when N ≥ 2, as −Δpu+up−1=λk(x)ur−1−h(x)uq−1.Here, h(x),k(x)>0 are Lebesgue measurable functions, 1<p<q<∞, p<r<min{p*,q} if p<N while p<r<q if p ≥ N, and λ>0 is a parameter. [ABSTRACT FROM AUTHOR]