Advances in Differential Equations

On the location of concentration points for singularly perturbed elliptic equations

Simone Secchi and Marco Squassina

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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.

Article information

Source
Adv. Differential Equations, Volume 9, Number 1-2 (2004), 221-239.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867974

Mathematical Reviews number (MathSciNet)
MR2099612

Zentralblatt MATH identifier
05054520

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B25: Singular perturbations 35B65: Smoothness and regularity of solutions 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Secchi, Simone; Squassina, Marco. On the location of concentration points for singularly perturbed elliptic equations. Adv. Differential Equations 9 (2004), no. 1-2, 221--239. https://projecteuclid.org/euclid.ade/1355867974


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