Differential and Integral Equations

Existence of radial solutions for a class of $p(x)$-Laplacian equations with critical growth

Claudianor O. Alves

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Using variational methods we establish the existence of solutions for the following class of $p(x)$-Laplacian equations: \begin{equation} -div(|\nabla u|^{p(x)-2}\nabla u) + |u|^{p(x)-2}u= \lambda |u|^{q(x)-2}u + |u|^{p^{*}(x)-2}u, \,\,\,\,\, \mathbb{R}^{N}, \tag*{(P)} \end{equation} where $\lambda \in (0, \infty)$ is a parameter and $p(x), q(x): \mathbb{R}^{N} \to \mathbb{R}$ are radial continuous functions satisfying $1 < p(x) < N$ and $p(x) < < q(x) < < p^{*}(x)= \frac{p(x)N}{N-p(x)}$.

Article information

Differential Integral Equations, Volume 23, Number 1/2 (2010), 113-123.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35A15: Variational methods 35H30: Quasi-elliptic equations 35B33: Critical exponents


Alves, Claudianor O. Existence of radial solutions for a class of $p(x)$-Laplacian equations with critical growth. Differential Integral Equations 23 (2010), no. 1/2, 113--123. https://projecteuclid.org/euclid.die/1356019390

Export citation