We study a nonlinear elliptic system of Lane--Emden type \[\left\{ \begin{array}{ll} -\Delta u\ =\ {\rm sgn}(v) |v|^{p-1} & \text{in $\R^{N}$,} \\ -\Delta v\ =\ - {\rm sgn}(u) |u|^{\frac1{p-1}} + f(u) & \text{in $\R^{N}$,} \\ u,\ v\ \rightarrow 0 \quad\text{as}\quad \left\vert x\right\vert \rightarrow +\infty,& \end{array}\right. \] which is equivalent to a fourth order elliptic equation. By using variational methods the existence of radial solutions of the given problem is proved. To this aim, new compact imbeddings are stated.

Elliptic systems in unbounded domains

CANDELA, Anna Maria;SALVATORE, Addolorata
2011

Abstract

We study a nonlinear elliptic system of Lane--Emden type \[\left\{ \begin{array}{ll} -\Delta u\ =\ {\rm sgn}(v) |v|^{p-1} & \text{in $\R^{N}$,} \\ -\Delta v\ =\ - {\rm sgn}(u) |u|^{\frac1{p-1}} + f(u) & \text{in $\R^{N}$,} \\ u,\ v\ \rightarrow 0 \quad\text{as}\quad \left\vert x\right\vert \rightarrow +\infty,& \end{array}\right. \] which is equivalent to a fourth order elliptic equation. By using variational methods the existence of radial solutions of the given problem is proved. To this aim, new compact imbeddings are stated.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/238
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