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2004 On the location of concentration points for singularly perturbed elliptic equations
Simone Secchi, Marco Squassina
Adv. Differential Equations 9(1-2): 221-239 (2004). DOI: 10.57262/ade/1355867974

Abstract

By exploiting a variational identity of Pohožaev-Pucci-Serrin type for solutions of class $C^1$, we get some necessary conditions for locating the peak-points of a class of singularly perturbed quasilinear elliptic problems in divergence form. More precisely, we show that the points where the concentration occurs, in general, must belong to what we call the set of weak-concentration points. Finally, in the semilinear case, we provide a new necessary condition which involves the Clarke subdifferential of the ground-state function.

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Simone Secchi. Marco Squassina. "On the location of concentration points for singularly perturbed elliptic equations." Adv. Differential Equations 9 (1-2) 221 - 239, 2004. https://doi.org/10.57262/ade/1355867974

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 05054520
MathSciNet: MR2099612
Digital Object Identifier: 10.57262/ade/1355867974

Subjects:
Primary: 35J60
Secondary: 35B25 , 35B65 , 58E05

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 1-2 • 2004
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