Abstract
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 ∈ ℝ and ξ ∈ ℝn. We prove the existence theorem for a solution u ∈ W 1,ploc (ℝn) under the condition p > n.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 133–147, 2006.
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Laptev, G.I. Existence of solutions of certain quasilinear elliptic equations in ℝN without conditions at infinity. J Math Sci 150, 2384–2394 (2008). https://doi.org/10.1007/s10958-008-0137-6
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DOI: https://doi.org/10.1007/s10958-008-0137-6