Radial Large Solutions to a Nonlinear Elliptic Problem in $\mathbb{R}^N$: On the Existence and Asymptotic Analysis.

Resumo

We consider the following elliptic equation
\[
\Delta_p u = g(x) h(u) \quad \text{in } \mathbb{R}^N,
\]
where \,
$
\Delta_p u \text{ is the } p-\mbox{Laplacian } \, \text{ with \,} N > p > 2,\quad
$
and the functions $h$ and $g$ satisfy appropriate assumptions. We establish existence results for large solutions and describe their asymptotic behavior as $|x| \to \infty$.