Advances in Differential Equations

On the location of concentration points for singularly perturbed elliptic equations

Simone Secchi and Marco Squassina

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.)


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.

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