On the Existence of a Component-wise Positive Radially Symmetric Solution for a Superlinear System
نویسنده
چکیده
The system under consideration is −∆u+ auu = u 3 − βuv, u = u(x), −∆v + avv = v 3 − βuv, v = v(x), x ∈ R, u||x|→∞ = v||x|→∞ = 0, where au, av and β are positive constants. We prove the existence of a componentwise positive smooth radially symmetric solution of this system. This result is a part of the results presented in the recent paper [1]; in our opinion, our method allows one to treat the problem simpler and shorter. AMS subject classification numbers (2000): 34B16, 34B18, 34B40, 35J50, 35J60, 35J65
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