Changfeng Gui

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics | 1993

Changfeng Gui; Fang Hua Lin

We study a semilinear boundary value problem with the feature that the vanishing boundary value makes the equation singular. We prove that the positive solution is in general Holder-continuous up to the boundary and has even better regularity in some special cases.

Communications in Partial Differential Equations | 2001

Nassif Ghoussoub; Changfeng Gui; Meijun Zhu

We consider the following singularly perturbed Neumann problem with the critical exponent: and show that as ε tends to zero, the peak of the solutions tends to the boundary of the domain provided that the energy of the solutions remains below a certain natural level. This phenomenon is very different from the subcritical case.

Communications on Pure and Applied Mathematics | 1994