Existence of solutions of certain quasilinear elliptic equations in ℝn without conditions at infinity

This paper deals with conditions for the existence of solutions of the equations considered in the whole space ℝn, n 2. The functions A i (x, u, ξ), i = 1, n, A 0(x, u), and f(x) can arbitrarily grow as |x| → ∞. These functions satisfy generalized conditions of the monotone operator theory in the arguments u and ξ ℝn. We prove the existence theorem for a solution u W loc 1,p (ℝn) under the condition p > n. © 2008 Springer Science+Business Media, Inc.