@article{de Araujo_Ercole_Vargas_2024, title={The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms}, volume={64}, url={https://apcz.umk.pl/TMNA/article/view/55334}, DOI={10.12775/TMNA.2023.061}, abstractNote={We consider, for $a,l\geq1$, $b,s,\alpha> 0$, and $p> q\geq1$, the
homogeneous Dirichlet problem for the equation $-\Delta_{p}u=\lambda
u^{q-1}+\beta u^{a-1}\left\vert
abla u\right\vert ^{b}+mu^{l-1}e^{\alpha
u^{s }$ in a smooth bounded domain $\Omega\subset\mathbb{R}^{N}$. We prove
that under certain setting of the parameters $\lambda$, $\beta$ and $m$ the
problem admits at least one positive solution. Using this result we prove that
if $\lambda,\beta> 0$ are arbitrarily fixed and $m$ is sufficiently small, then
the problem has a positive solution $u_{p}$, for all $p$ sufficiently large.
In addition, we show that $u_{p}$ converges uniformly to the distance function
to the boundary of $\Omega$, as $p\rightarrow\infty$. This convergence result
is new for nonlinearities involving a convection term.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={de Araujo, Anderson L. A. and Ercole, Grey and Vargas, Julio C. Lanazca}, year={2024}, month={Sep.}, pages={339–359} }