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On the location of concentration points for singularly perturbed elliptic equations

Simone Secchi·Marco Squassina
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Abstract

By means of a variational identity of Pohožaev-Pucci-Serrin type for solutions of class $C^1$ recently obtained, we give some necessary conditions for locating the concentration points for a class of quasi-linear elliptic problems in divergence form. More precisely we show that the points where the concentration occurs must be critical, either in a generalized or in the classical sense, for a suitable ground state function.

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Simone Secchi, Marco Squassina. 2003-11-19. On the location of concentration points for singularly perturbed elliptic equations. https://arxiv.org/abs/math/0306287

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