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QUASILINEAR PROBLEMS WITH THE COMPETITION BETWEEN CONVEX AND CONCAVE NONLINEARITIES AND VARIABLE POTENTIALS
The purpose of this paper is to prove some existence and non-existence theorems for the nonlinear elliptic problems of the form -Δ p u = λk(x)u q ± h(x)u σ if x ∈ Ω, subject to the Dirichlet condition u = 0 on ∂Ω. In the proof of our results …