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We study the existence of positive radial solutions of semilinear elliptic equations . By using a variational method and finite balls approach, we prove that there exists a positive radial solution with finite energy on
provided that K satisfies the following conditions (i)
for small r > 0, β > 0 and α∊(0,n), (ii) K(r) ≥ 0 for large r and
and (iii)
. Some existence theorems of positive radial and non-radial solutions on
also obtained for equations
.
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