Exact Multiplicity Result for the Perturbed Scalar Curvature Problem in R N ( N ≥ 3 )
نویسندگان
چکیده
Let D1,2(RN ) denote the closure of C∞ 0 (R N ) in the norm ‖u‖2 D1,2(RN ) = ∫ RN |∇u|2. Let N ≥ 3 and define the constants αN = N(N − 2) and CN = (N(N − 2)) N−2 4 . Let K ∈ C2(RN ). We consider the following problem for ε ≥ 0 : (Pε) ⎪⎨⎪⎩ Find u ∈ D1,2(RN ) solving : −∆u = αN (1 + εK(x))u N+2 N−2 , u > 0 } in RN . We show an exact multiplicity result for (Pε) for all small ε > 0.
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