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The multiplicity of radial solutions to a higher dimensional scalar-field equation with the Robin condition is discussed. Unlike our previous results, multiplicity of positive solutions is obtained near l 1⁄4 0. Moreover, one solution has a blowing-up behavior and the other is uniformly bounded. A key point is the transformation of the original problem to the exterior Neumann problem and the socalled openness argument.

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Multiplicity of Positive Radial Solutions to a Higher Dimensional Scalar-Field Equation Involving the Critical Sobolev Exponent under the Robin Condition