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- W4322827084 abstract "We consider, for $a,lgeq1,$ $b,s,alpha>0,$ and $p>qgeq1,$ the homogeneous Dirichlet problem for the equation $-Delta_{p}u=lambda u^{q-1}+beta u^{a-1}leftvert nabla urightvert ^{b}+mu^{l-1}e^{alpha u^{s}}$ in a smooth bounded domain $Omegasubsetmathbb{R}^{N}.$ 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 $prightarrowinfty.$ This convergence result is new for nonlinearities involving a convection term." @default.
- W4322827084 created "2023-03-03" @default.
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- W4322827084 date "2023-02-28" @default.
- W4322827084 modified "2023-09-29" @default.
- W4322827084 title "The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms" @default.
- W4322827084 doi "https://doi.org/10.48550/arxiv.2303.00140" @default.
- W4322827084 hasPublicationYear "2023" @default.
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