Advances in Differential Equations

Least energy solutions for critical growth equations with a lower order perturbation

Alberto Ferrero

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We study existence and nonexistence of least energy solutions of a quasilinear critical growth equation with degenerate $m$-Laplace operator in a bounded domain in $\mathbb{R}^n$ with $n>m>1$. Existence and nonexistence of solutions of this problem depend on a lower order perturbation and on the space dimension $n$. Our proofs are obtained with critical point theory and the lack of compactness, due to critical growth condition, is overcome by constructing minimax levels in a suitable compactness range.

Article information

Adv. Differential Equations, Volume 11, Number 10 (2006), 1167-1200.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35J70: Degenerate elliptic equations 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Ferrero, Alberto. Least energy solutions for critical growth equations with a lower order perturbation. Adv. Differential Equations 11 (2006), no. 10, 1167--1200.

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