Existence and location of solutions to the Dirichlet problem for a class of nonlinear elliptic equations Original Research Article

In a bounded open set Ω ⊂ Rn, we consider a Dirichlet problem of the type View the MathML source View the MathML source , where, in particular, f(x,·), g(x,·) have a subcritical growth, and h(x,·), l(x,·) are nonincreasing, with a critical growth. It is our aim to show that, for explicitly determined Ψ : View the MathML source, and ϕ :]r∗,+∞[→ [0,+∞[, with View the MathML source ψ, for each r > r∗ and each μ > ϕ(r), the above problem has at least one weak solution that lies in ψ−1(]−∞,r[). A major novelty is just the precise determination of ϕ.