Uniqueness and nondegeneracy of sign-changing radial solutions to an almost critical elliptic problem
نویسندگان
چکیده
where 1 < p < N+2 N−2 , N ≥ 3. It is well-known that this equation has a unique positive radial solution. The existence of sign-changing radial solutions with exactly k nodes is also known. However the uniqueness of such solutions is open. In this paper, we show that such sign-changing radial solution is unique when p is close to N+2 N−2 . Moreover, those solutions are non-degenerate, i.e., the kernel of the linearized operator is exactly N -dimensional.
منابع مشابه
Uniqueness and nondegeneracy of sign-changing radial solutions of an almost critical problem
∗Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada, V6T 1Z2. Email: [email protected] †Department of Mathematics University of British Columbia, Vancouver, B.C., Canada, V6T 1Z2. Email: [email protected] ‡Departamento de Ingenieŕıa Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile. Email:...
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