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• W2953067717 abstract "We study a class of fractional elliptic problems of the form $Ds u= f(u)$ in the half space $R^N_+:={x in R^N::: x_1>0}$ with the complementary Dirichlet condition $u equiv 0$ in $R^N setminus R^N_+$. Under mild assumptions on the nonlinearity $f$, we show that bounded positive solutions are increasing in $x_1$. For the special case $f(u)=u^q$, we deduce nonexistence of positive bounded solutions in the case where $q ge 1$ and $q<frac{N-1+2s}{N-1-2s}$ if $N ge 1+2s$. We do not require integrability assumptions on the solutions we study." @default.
• W2953067717 created "2019-06-27" @default.
• W2953067717 creator A5062208839 @default.
• W2953067717 creator A5063408184 @default.
• W2953067717 date "2013-09-27" @default.
• W2953067717 modified "2023-10-16" @default.
• W2953067717 title "Monotonicity and nonexistence results for some fractional elliptic problems in the half space" @default.
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• W2953067717 hasPublicationYear "2013" @default.
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