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Funkcialaj Ekvacioj
Vol. 54 (2011) No. 3 P 439-449



In this article we consider the system of equations Δui = pi(x)fi(u1,...,ud) for i = 1,...,d on RN, N ≥ 3 and d ∈ {1,2,3,4,...}. We prove that the considered system has a bounded positive entire solution under some conditions on pi and fi. Also, we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation. Furthermore, a non-radially symmetric solution is obtained by using a lower and upper solution method.

Copyright © 2011 by the Division of Functional Equations, The Mathematical Society of Japan

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