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Solutions for a Schrödinger-Kirchhoff Equation with Indefinite Potentials

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Abstract

We deal with the equation

$$-\left( 1+\int\nolimits_{\mathbb{R}^3}|\nabla u|^2 dx\right)\Delta u + V(x)u=a(x)|u|^{p-1}u,\quad x\in {\mathbb{R}}^3,$$

with p ∈ (3, 5). Under some conditions on the sign-changing potentials V and a we obtain a nonnegative ground state solution. In the radial case we also obtain a nodal solution.

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Authors and Affiliations

  1. Departamento de Ciências Exatas e Aplicadas, Universidade Federal do Rio Grande do Norte, 59300-00, Caicò, RN, Brazil

    Alex M. Batista

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

    Marcelo F. Furtado

Authors
  1. Alex M. Batista
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  2. Marcelo F. Furtado
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Correspondence to Marcelo F. Furtado.

Additional information

The authors were partially supported by CNPq/Brazil. The second author was also supported by FAPDF/Brazil.

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Batista, A.M., Furtado, M.F. Solutions for a Schrödinger-Kirchhoff Equation with Indefinite Potentials. Milan J. Math. 86, 1–14 (2018). https://doi.org/10.1007/s00032-018-0276-2

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  • DOI: https://doi.org/10.1007/s00032-018-0276-2

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