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Qualitative Properties of Solutions to Elliptic Equations with Nonpower Nonlinearities in ℝ n

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We consider a class of anisotropic elliptic equations with nonpower nonlinearities. We establish the existence of a solution in the local Sobolev–Orlicz spaces without conditions on the data growth at infinity. We find sufficient uniqueness conditions, obtain estimates characterizing the behavior of the solution at infinity, and prove the continuous dependence of the solution on the right-hand side of the equation.

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Authors and Affiliations

  1. Sterlitamak Branch of Bashkir State University, 37, Lenina Pr., Sterlitamak, 453103, Russia

    L. M. Kozhevnikova

  2. Tyumen State University, 6, Volodarskogo St., Tyumen, 625003, Russia

    A. A. Nikitina

Authors
  1. L. M. Kozhevnikova
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  2. A. A. Nikitina
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Correspondence to L. M. Kozhevnikova.

Additional information

Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 16, No. 2, 2016, pp. 26-40.

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Kozhevnikova, L.M., Nikitina, A.A. Qualitative Properties of Solutions to Elliptic Equations with Nonpower Nonlinearities in ℝ n . J Math Sci 228, 395–408 (2018). https://doi.org/10.1007/s10958-017-3630-y

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  • DOI: https://doi.org/10.1007/s10958-017-3630-y

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