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Existence of positive entire solutions of fully nonlinear elliptic equations

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Abstract

In this paper we try to generalize a well known result due to Brezis on the existence of weak solutions in the whole space to second-order fully nonlinear equations with an absorption term satisfying a Keller–Osserman condition plus an additive external source without growth condition at infinity. We also discuss constant sign solutions.

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Acknowledgements

The author wish to thank the referees for useful comments. The author also thanks GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le Applicazioni) for partial support.

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  1. Department of Civil Engineering, Università di Salerno, 84084, Fisciano, Salerno, Italy

    Antonio Vitolo

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  1. Antonio Vitolo
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Vitolo, A. Existence of positive entire solutions of fully nonlinear elliptic equations. J Elliptic Parabol Equ 4, 293–304 (2018). https://doi.org/10.1007/s41808-018-0019-0

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  • DOI: https://doi.org/10.1007/s41808-018-0019-0

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