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Slowly decaying radial solutions of an elliptic equation with subcritical and supercritical exponents

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Abstract

We study radial solutions of the problem

$$\Delta u + {u^p} + {u^q} = 0,\;u > 0\;in\;{\mathbb{R}^N}$$

, where N ≥ 3 and

$$\frac{N}{{N - 2}} < p < \frac{{N + 2}}{{N - 2}} < q$$

. We show that if p is close to N/(N-2), q is close to (N +2)/(N-2), and a certain relation holds between them, then the problem has slowly decaying solutions.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807, CNRS), Universidad de Chile, Casilla 170/3 Correo 3, Santiago, Chile

    Juan Dávila

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

    Ignacio Guerra

Authors
  1. Juan Dávila
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  2. Ignacio Guerra
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Corresponding author

Correspondence to Juan Dávila.

Additional information

J. D. was supported by Fondecyt 1130360 and Fondo Basal CMM.

I. G. was supported by Fondecyt 1130790.

J. D. and I. G. were also supported byMillennium Nucleus Center for Analysis of PDE NC130017.

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Dávila, J., Guerra, I. Slowly decaying radial solutions of an elliptic equation with subcritical and supercritical exponents. JAMA 129, 367–391 (2016). https://doi.org/10.1007/s11854-016-0025-9

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  • DOI: https://doi.org/10.1007/s11854-016-0025-9

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