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 A; SALVATORE A. - In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. - ISSN 1747-6933. - 56(2011), pp. 1143-1153.
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Titolo: | Elliptic systems in unbounded domains |
Autori: | |
Data di pubblicazione: | 2011 |
Rivista: | |
Citazione: | Elliptic systems in unbounded domains / CANDELA A; SALVATORE A. - In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. - ISSN 1747-6933. - 56(2011), pp. 1143-1153. |
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. |
Handle: | http://hdl.handle.net/11586/238 |
Appare nelle tipologie: | 1.1 Articolo in rivista |