TY - JOUR
AU - de Araujo, Anderson L. A.
AU - Ercole, Grey
AU - Vargas, Julio C. Lanazca
PY - 2024/09/21
Y2 - 2024/11/01
TI - The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 64
IS - 1
SE -
DO - 10.12775/TMNA.2023.061
UR - https://apcz.umk.pl/TMNA/article/view/55334
SP - 339 - 359
AB - We consider, for $a,l\geq1$, $b,s,\alpha> 0$, and $p> q\geq1$, thehomogeneous Dirichlet problem for the equation $-\Delta_{p}u=\lambdau^{q-1}+\beta u^{a-1}\left\vert
abla u\right\vert ^{b}+mu^{l-1}e^{\alphau^{s}}$ in a smooth bounded domain $\Omega\subset\mathbb{R}^{N}$. We provethat under certain setting of the parameters $\lambda$, $\beta$ and $m$ theproblem admits at least one positive solution. Using this result we prove thatif $\lambda,\beta> 0$ are arbitrarily fixed and $m$ is sufficiently small, thenthe problem has a positive solution $u_{p}$, for all $p$ sufficiently large.In addition, we show that $u_{p}$ converges uniformly to the distance functionto the boundary of $\Omega$, as $p\rightarrow\infty$. This convergence resultis new for nonlinearities involving a convection term.
ER -