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Existence of Positive Solution for a Singular Elliptic Problem with an Asymptotically Linear Nonlinearity

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Abstract

In this paper, we consider the existence of positive solutions for a singular elliptic problem involving an asymptotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison techniques, we show the existence, uniqueness, non-existence, and regularity of the solutions. We also obtain a bifurcation-type result.

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Acknowledgements

The author would like to thank the anonymous reviewer for her/his careful reading of the manuscript and many comments and suggestions.

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  1. Departamento de Matemática, Universidade de Brasília, Brasília, DF, 70910-900, Brazil

    Ricardo Lima Alves

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  1. Ricardo Lima Alves
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Correspondence to Ricardo Lima Alves.

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The author was supported by CNPq/Brazil Proc. No. 141110/2017-1.

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Lima Alves, R. Existence of Positive Solution for a Singular Elliptic Problem with an Asymptotically Linear Nonlinearity. Mediterr. J. Math. 18, 4 (2021). https://doi.org/10.1007/s00009-020-01646-9

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  • DOI: https://doi.org/10.1007/s00009-020-01646-9

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