Abstract
Positive radial solutions of a semilinear elliptic equation △u+g(r)u+h(r)u p=0, where r=|x|, xεR n, and p>1, are studied in balls with zero Dirichlet boundary condition. By means of a generalized Pohožaev identity which includes a real parameter, the uniqueness of the solution is established under quite general assumptions on g(r) and h(r). This result applies to Matukuma's equation and the scalar field equation and is shown to be sharp for these equations.
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Yanagida, E. Uniqueness of positive radial solutions of △u+g(r)u+h(r)u p=0 in Rn . Arch. Rational Mech. Anal. 115, 257–274 (1991). https://doi.org/10.1007/BF00380770
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DOI: https://doi.org/10.1007/BF00380770