@Article{JPDE-26-3,
author = {Thanh, Nguyen, Chung},
title = {On an Anisotropic Equation with Critical Exponent and Non-standard Growth Condition},
journal = {Journal of Partial Differential Equations},
year = {2013},
volume = {26},
number = {3},
pages = {217--225},
abstract = {<p>Using variational methods, we prove the existence of a nontrivial weak solution for the problem \begin{align*} \left\{ &nbsp;\begin{array}{ll} -\sum_{i=1}^N\partial_{x_i}\Big(|\partial_{x_i}u|^{p_i-2}\partial_{x_i}u\Big) =\lambda a(x)|u|^{q(x)-2}u+|u|^{p^\ast-2}u, &amp; \text{ in } \Omega, &nbsp;\\ u = 0, &amp; \text{ in } \partial\Omega, \end{array} \right. \end{align*} where $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) is a bounded domain with smooth boundary $\partial\Omega$, $2 \leq p_i &lt; N$, $i = \overline{1, N}$, $q: \overline \Omega \to (1, p^\ast)$ is a continuous function, $p^\ast=\frac{N}{\sum_{i=1}^N \frac{1}{p_i}-1}$ is the critical exponent for this class of problem, and $\lambda$ is a parameter.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v26.n3.2},
url = {https://global-sci.com/article/88329/on-an-anisotropic-equation-with-critical-exponent-and-non-standard-growth-condition}
}