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This paper gives the growth property of certain harmonic functions at infinity in an n-dimensional cone, which generalize the results obtained by Huang and Qiao (Abstr. Appl. Anal. 2012:203096, ), Xu et al. (Bound. Value Probl. 2013:262, ), Yang and Ren (Proc. Indian Acad. Sci. Math. Sci. 124(2): 175-178, ) and Zhao and Yamada (J. Inequal. Appl. 2014:497, ) to the conical case. [ABSTRACT FROM AUTHOR]

Let F be a family of solutions of Laplace equations in a domain D and for each f ∈ F , f has only zeros of multiplicity at least k. Let n be a positive integer and such that n ≥ 1 + 1 + 4 k (k + 1) 2 2 k . Let a be a complex number such that a ≠ 0 . If for each pair of functions f and g in F , f n f (k) and g n g (k) share a value in D, then F is normal in D. [ABSTRACT FROM AUTHOR]