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- W4239988122 abstract "Synopsis Let Ω be a bounded domain in ℝ 2 . The study, begun in Keady [ 13 ], of the boundary-value problem, for (λ/ k , ψ), is continued. Here Δ denotes the Laplacian, H is the Heaviside step function and one of λ or k is a given positive constant. The solutions considered always have ψ > 0 in Ω and λ/ k > 0, and have cores In the special case Ω = B (0, R ), a disc, the explicit exact solutions of the branch τ e have connected cores A and the diameter of A tends to zero when the area of A tends to zero. This result is established here for other convex domains Ω and solutions with connected cores A. An adaptation of the maximum principles and of the domain folding arguments of Gidas, Ni and Nirenberg [ 9 ] is an important step in establishing the above result." @default.
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- W4239988122 date "1987-01-01" @default.
- W4239988122 modified "2023-09-28" @default.
- W4239988122 title "An elliptic boundary-value problem with a discontinuous nonlinearity, II" @default.
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- W4239988122 doi "https://doi.org/10.1017/s0308210500021880" @default.
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