Combined effects in nonlinear problems arising in the study of anisotropic continuous media

We are concerned with the Lane–Emden–Fowler equation −Δu=λk(x)uq±h(x)up in ΩΩ, subject to the Dirichlet boundary condition u=0u=0 on ∂Ω∂Ω, where ΩΩ is a smooth bounded domain in RNRN, kk and hh are variable potential functions, and 0