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The existence and uniqueness of positive radial solutions of the equations of the type [IML0001] in BR, p>1 with Dirichlet condition are proved for λ large enough and f satisfying a condition[IML0002] is non-decreasing on [IML0003] It is also proved that all the positive solutions in C1 0(BR) of the above equations are radially symmetric solutions for f satisfying [IML0004] and λ large enough.
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