The existence and multiplicity of classical positive solutions for a singular nonlinear elliptic problem with any growth exponents

In this paper we consider a class of singular elliptic boundary problems −Δu=λuβ+p(x)u−γ,u>0inΩ,u=0on∂Ω with 1<β1<β, 0<γ<10<γ<1 and p∈C0α(Ω¯)(0<α<1). We emphasize that there is no restriction on the boundedness of ββ from above. By means of the approximating variational arguments and truncation, two classical positive solutions are obtained.