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- W2534781100 abstract "In this paper we investigate in a variational setting, the ellipticboundary value problem $-Delta u={textt{sign}u}/{|u|^{alpha+1}}$ in$Omega$, $u=0$ on $partialOmega$, where $Omega$ is an open connectedbounded subset of ${mathbb R}^N$, and $alpha> 0$. For the positive solution,which is checked as a minimum point of the formally associatedfunctional $$E(u)=frac 12int_Omega|nabla u|^2+frac{1}{alpha}int_Omega frac1{|u|^alpha}, $$we prove dependenceon the domain $Omega$. Moreover, an approximative functional $E_varepsilon$ isintroduced, and an upper bound for the sequence of mountain pass points $u_varepsilon$ of $E_varepsilon$, as $varepsilonto 0$, is given. For the onedimensionalcase, all sign-changing solutions of$-u''={text{sign}u}/{|u|^{alpha+1}}$ are characterized by theirnodal set as the mountain pass point and $n$-saddle points ($n> 1$) ofthe functional $E$." @default.
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- W2534781100 date "2006-03-01" @default.
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- W2534781100 title "On a second order boundary value problem with singular nonlinearity" @default.
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- W2534781100 doi "https://doi.org/10.12775/tmna.2006.001" @default.
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