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- W2018106129 abstract "We analyze the semilinear problem Δu L + ƒ(u L ) = 0 in ]0, 2L[×Ω, u L = 0 at ∂(]0, 2L[×Ω) , where Ω ⊂ R n − 1 is a bounded, smooth domain and ƒ is a given nonlinearity, in the limit L → ∞. The solutions of that problem are related to those of the ( n − 1)-dimensional problem Δv + ƒ(v) = 0 in Ω, v = 0 at ∂Ω. In particular, necessary and sufficient conditions on a given solution of the latter, v , are given for the former to have a solution, u L , such that u L ( x 1 , x 2 , …, x n ) → v ( x 2 , …, x n ) as L → ∞, in most part of the cylinder ]0, 2L[× Ω . Related bifurcation problems and some generalizations are also considered." @default.
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- W2018106129 title "Multiple solutions of some semilinear elliptic equations in slender cylindrical domains" @default.
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- W2018106129 doi "https://doi.org/10.1016/0022-0396(92)90113-2" @default.
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