Advances in Differential Equations

Concentration phenomena in elliptic problems with critical and supercritical growth

Riccardo Molle and Angela Pistoia

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This paper deals with the existence of positive solutions of problem $-\Delta u=u^{N+2\over N-2}+{\varepsilon} w(x)u^q $, with Dirichlet zero boundary condition on $\Omega$ (a bounded domain in $\mathbb R^N$), when $q\geq 1$ and $q\neq{N+2\over N-2}$. We study the existence of solutions which blow-up and concentrate at a single point of $\Omega$ whose location depends on the Robin function and on the coefficient $w$ of the perturbed term.

Article information

Adv. Differential Equations, Volume 8, Number 5 (2003), 547-570.

First available in Project Euclid: 19 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B25: Singular perturbations 35B33: Critical exponents 35B40: Asymptotic behavior of solutions


Molle, Riccardo; Pistoia, Angela. Concentration phenomena in elliptic problems with critical and supercritical growth. Adv. Differential Equations 8 (2003), no. 5, 547--570.

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