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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Two solutions for a planar equation with combined nonlinearities and critical growth
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by Marcelo F. Furtado PDF
Proc. Amer. Math. Soc. 147 (2019), 4397-4408 Request permission

Abstract:

We prove the existence of two nonnegative nontrivial solutions for the equation \begin{equation*} -\Delta u -\frac {1}{2} (x\cdot \nabla u) = \lambda a(x)|u|^{q-2}u+f(u),\qquad x\in \mathbb {R}^2, \end{equation*} where $1<q<2$, $a$ is indefinite in sign, and the function $f(s)$ behaves like $e^{\alpha s^2}$ at infinity. The results hold for small values of the parameter $\lambda >0$.
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Additional Information
  • Marcelo F. Furtado
  • Affiliation: Departamento de Matemática, Universidade de Brasília, 70910-900, Braília-Df, Brazil
  • MR Author ID: 673056
  • Email: mfurtado@unb.br
  • Received by editor(s): January 23, 2019
  • Published electronically: June 10, 2019
  • Additional Notes: The author was partially supported by CNPq/Brazil and FAPDF/Brazil
  • Communicated by: Joachim Krieger
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4397-4408
  • MSC (2010): Primary 35J60; Secondary 35B33
  • DOI: https://doi.org/10.1090/proc/14677
  • MathSciNet review: 4002551