Description

• Title:
  The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms
• Creator:
  de Araujo, Anderson L. A.;
  Ercole, Grey;
  Vargas, Julio C. Lanazca
• Description:
  We consider, for $a,l\geq1$, $b,s,\alpha> 0$, and $p> q\geq1$, the homogeneous Dirichlet problem for the equation $-\Delta_{p}u=\lambda u^{q-1}+\beta u^{a-1}\left\vert \nabla u\right\vert ^{b}+mu^{l-1}e^{\alpha u^{s}}$ 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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Anderson L. A. de Araujo, Grey Ercole, Julio C. Lanazca Vargas;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.09.21
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 1 (September 2024); 339 - 359;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55334/39772 ;https://apcz.umk.pl/TMNA/article/view/55334/39773
• Subject:
  Convection term;
  distance function;
  exponential term;
  gradient estimate;
  Primary: 35A01, 35B40;
  Secondary: 35J92
• Identifier: https://apcz.umk.pl/TMNA/article/view/55334
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other