The method of upper and lower solutions for a Lidstone boundary value problem

Yanping Guo; Ying Gao

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Displaying similar documents to “The method of upper and lower solutions for a Lidstone boundary value problem”

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Nonuniqueness for some linear oblique derivative problems for elliptic equations

Gary M. Lieberman (1999)

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It is well-known that the “standard” oblique derivative problem, $Δ u = 0$ in $Ω$ , $\partial u / \partial ν - u = 0$ on $\partial Ω$ ( $ν$ is the unit inner normal) has a unique solution even when the boundary condition is not assumed to hold on the entire boundary. When the boundary condition is modified to satisfy an obliqueness condition, the behavior at a single boundary point can change the uniqueness result. We give two simple examples to demonstrate what can happen.