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An ODE approach for fractional Dirichlet problems with gradient nonlinearity

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Abstract

In the present work we study existence of solutions of fractional Dirichlet problems in the presence of coercive gradient terms with growth comparable and slightly bigger than the order of the nonlocal elliptic operator. We develop a 1-dimensional reduction that allows us to construct barriers via ODE methods and therefore to obtain existence results based on an integral criterion that resembles the classical second-order case.

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Acknowledgements

G. Dávila was partially supported by Fondecyt Grant No. 11150880. E. Topp was partially supported by Conicyt PIA Grant No. 79150056, and Fondecyt Grant No. 11160817. A. Quaas was partially supported by Fondecyt Grant No. 1151180, Programa Basal, CMM. U. de Chile and Millennium Nucleus Center for Analysis of PDE NC130017.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla: v-110, Avda. España 1680, Valparaiso, Chile

    Gonzalo Dávila & Alexander Quaas

  2. Departamento de Matemática y C.C., Universidad de Santiago de Chile, Casilla 307, Santiago, Chile

    Erwin Topp

Authors
  1. Gonzalo Dávila
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  2. Alexander Quaas
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  3. Erwin Topp
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Correspondence to Erwin Topp.

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Dávila, G., Quaas, A. & Topp, E. An ODE approach for fractional Dirichlet problems with gradient nonlinearity. Math. Z. 291, 85–111 (2019). https://doi.org/10.1007/s00209-018-2074-5

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  • DOI: https://doi.org/10.1007/s00209-018-2074-5

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