MR2297949 Kabeya, Yoshitsugu and Morishita, Hiroshi Yoshitsugu KABEYA and Hiroshi MORISHITA Multiplicity of Positive Radial Solutions to a Higher Dimensional Scalar-Field Equation Involving the Critical Sobolev Exponent under the Robin Condition Funkcialaj Ekvacioj. Serio Internacia 49 2006 469--503 http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-3/49_469.pdf http://www.ams.org/mathscinet-getitem?mr=MR2297949 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 $\lambda=0$. 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 so-called openness argument. Multiplicity of solutions, Bifurcation diagrams, Radial solutions. 35J25, 35B40. 49-469 2006 Multiplicity of Positive Radial Solutions to a Higher Dimensional Scalar-Field Equation Involving the Critical Sobolev Exponent under the Robin Condition KABEYA, Yoshitsugu and MORISHITA, Hiroshi Yoshitsugu KABEYA and Hiroshi MORISHITA
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