Abstract
Let B R be the ball centered at the origin with radius R in ℝN (N≥2). In this paper we study the existence of solution for the following elliptic system
where λ > 0, µ > 0 p ≥ 2, q ≥ 2, ν is the unit outward normal at the boundary ∂B R . Under certain assumptions on κ(|x|), using variational methods, we prove the existence of a positive and radially increasing solution for this problem without growth conditions on the nonlinearity.
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Liu, Zy. On the existence of solutions for an elliptic system of equations with arbitrary order growth. Acta Math. Appl. Sin. Engl. Ser. 29, 415–424 (2013). https://doi.org/10.1007/s10255-013-0224-4
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DOI: https://doi.org/10.1007/s10255-013-0224-4