On a class of quasilinear problems with sign-changing nonlinearities Original Research Article

We prove existence and nonexistence of positive solutions for the quasilinear problem View the MathML source-Δpu+mψp(u)=λa(x)f(u)inΩ,u=0on∂Ω, Turn MathJax on where View the MathML sourceΔpu=div(|∇u|p-2∇u), ψp(u)=|u|p-2uψp(u)=|u|p-2u, p>1p>1, m⩾0m⩾0, ΩΩ is a bounded domain in RNRN, and the coefficient a(x)a(x), is allowed to change sign.