TY - JOUR
T1 - On a Nonhomogeneous $N$-Laplacian Problem with Double Exponential Critical Growth
AU - Chen , Wenjing
AU - Wang , Zexi
JO - Journal of Partial Differential Equations
VL - 1
SP - 80
EP - 100
PY - 2025
DA - 2025/04
SN - 38
DO - http://doi.org/10.4208/jpde.v38.n1.5
UR - https://global-sci.org/intro/article_detail/jpde/23953.html
KW - $N$-Laplacian, Trudinger-Moser type inequality, double exponential critical growth, variational methods.
AB - <p style="text-align: justify;">This paper is devoted to studying the existence and multiplicity of nontrivial
solutions for the following boundary value problem $$\begin{cases} -{\rm div}(\omega(x)|\nabla u(x)|^{N-2}\nabla u(x))=f(x,u)+\epsilon h(x), &amp; {\rm in} \ B; \\ u=0, &amp; {\rm on} \ \partial B, \end{cases}$$where $B$ is the unit ball in $\mathbb{R}^N,$ the radial positive weight $ω(x)$ is of logarithmic type
function, the functional $f(x,u)$ is continuous in $B×\mathbb{R}$ and has double exponential critical growth, which behaves like ${\rm exp}\{e^{\alpha|u|^{\frac{N}{N-1}}} \}$ as $|u| → ∞$ for some $α &gt; 0.$ Moreover, $ϵ&gt;0,$ and the radial function $h$ belongs to the dual space of $W^{1,N}_{0,rad}(B)$ $h\ne 0.$</p>