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We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system where is a small positive parameter; , and are radially symmetric potentials; Q is a -homogeneous function and p is subcritical, that is, 1 , where is the critical Sobolev exponent for .

POSITIVE RADIAL SOLUTIONS FOR A CLASS OF ELLIPTIC SYSTEMS CONCENTRATING ON SPHERES WITH POTENTIAL DECAY