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Oscillation theorems of quasilinear elliptic equations with arbitrary nonlinearities

In asymptotic theory of differential equations it is an important problem to determine whether solutions of equations under consideration are oscillatory or not. The aim of this paper is to establish oscillation criteria for solutions of quasilinear elliptic equations of the form ∆mu + a(x)f(u) = 0, (1.1) where ∆m denotes the m−Laplace operator: ∆mu = div(|Du|m−2Du),m > 1. To begin with we give the definition of oscillation precisely: