Abstract
We show the existence of a positive solution \(u_{p}\) for a Dirichlet p-Laplacian problem with nonlinearity involving an exponential term that can be supercritical. We determine the asymptotic behavior of \(u_{p}\) as \(p\rightarrow 1^{+}\) and \(p\rightarrow +\infty \), which are related to the Cheeger constant and the distance function to the boundary, respectively. Furthermore, we also prove a nonexistence result concerning the range of the parameter \(\lambda \).
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Acknowledgements
Anderson L. A. de Araujo was partially supported by FAPEMIG/Brazil (Grant No. RED-00133-21) and by CNPq/Brazil. Grey Ercole was partially supported by FAPEMIG/Brazil PPM-00137-18 and by CNPq/Brazil 305578/2020-0. Marcelo Montenegro was partially supported by CNPq and by FAPESP.
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This work was supported by FAPEMIG grant number (RED-00133-21)
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de Araujo, A.L.A., Ercole, G. & Montenegro, M. Asymptotic Behavior Related to Cheeger Constant for Solutions of an Exponentially Growth Equation. Results Math 79, 47 (2024). https://doi.org/10.1007/s00025-023-02077-0
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DOI: https://doi.org/10.1007/s00025-023-02077-0