We study the existence of weak solutions for a nonlinear elliptic system of Lane–Emden type $−Δu = sgn(v)|v|^{p−1}$ in $R^N$ , $−Δv = −ρ(x)sgn(u)|u|^{1/{p−1}} + f(x, u)$ in $R^N$ , u, v → 0 as |x| → +∞, by means of the Mountain Pass Theorem and some compact imbeddings in weighted Sobolev spaces.
Weighted elliptic systems of Lane-Emden type in unbounded domains,
SALVATORE, Addolorata
2012-01-01
Abstract
We study the existence of weak solutions for a nonlinear elliptic system of Lane–Emden type $−Δu = sgn(v)|v|^{p−1}$ in $R^N$ , $−Δv = −ρ(x)sgn(u)|u|^{1/{p−1}} + f(x, u)$ in $R^N$ , u, v → 0 as |x| → +∞, by means of the Mountain Pass Theorem and some compact imbeddings in weighted Sobolev spaces.File in questo prodotto:
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