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- W2891920187 abstract "In this paper we study the existence of minimizers for $$ F(u) = 1/2int_{R^3} |nabla u|^2 dx + 1/4int_{R^3}int_{R^3}frac{| u(x) |^2| u(y) |^2}{| x-y |}dxdy-frac{1}{p}int_{R^3}| u |^p dx$$ on the constraint $$S(c) = {u in H^1(R^3) : int_{R^3}|u|^2 dx = c },$$ where $c>0$ is a given parameter. In the range $p in [3, 10/3]$ we explicit a threshold value of $c>0$ separating existence and non-existence of minimizers. We also derive a non-existence result of critical points of $F(u)$ restricted to $S(c)$ when $c>0$ is sufficiently small. Finally, as a byproduct of our approaches, we extend some results of cite{CJS} where a constrained minimization problem, associated to a quasilinear equation, is considered." @default.
- W2891920187 created "2018-09-27" @default.
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- W2891920187 date "2012-03-27" @default.
- W2891920187 modified "2023-09-24" @default.
- W2891920187 title "Sharp non-existence results of prescribed $L^2$-norm solutions for a class of stationary Schrodinger-Poisson equations" @default.
- W2891920187 hasPublicationYear "2012" @default.
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