The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms
Year: 2024
Type: article
Abstract: 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.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Awards: G2604241884, ANÁLISE DE EQUAÇÕES DIFERENCIAIS PARCIAIS E ALGUMAS APLICAÇÕES, G3338836700, G4373714938, REDE MINEIRA DE MATEMÁTICA (RMMAT-MG), G4955648311, G5153739147, G5200809177, COMPORTAMENTO ASSINTÓTICO EM PROBLEMAS QUASILINEARES ELÍPTICOS, G5662065345, G6801585736, G7747164569, G8920261182, G899089029, G933539513
OpenAlex ID: W4402782344