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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Nodal solutions for some singularly perturbed Dirichlet problems
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by Teresa D’Aprile and Angela Pistoia PDF
Trans. Amer. Math. Soc. 363 (2011), 3601-3620 Request permission

Abstract:

We consider the equation $-\varepsilon ^2 \Delta u+u=f(u)$ in a bounded, smooth domain $\Omega \subset \Bbb R^N$ with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of $\Omega$. The nonlinearity $f$ grows superlinearly and subcritically. We do not require symmetry conditions on the geometry of the domain.
References
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Additional Information
  • Teresa D’Aprile
  • Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy
  • Email: daprile@mat.uniroma2.it
  • Angela Pistoia
  • Affiliation: Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, via Antonio Scarpa 16, 00161 Roma, Italy
  • Email: pistoia@dmmm.uniroma1.it
  • Received by editor(s): December 16, 2008
  • Received by editor(s) in revised form: October 1, 2009
  • Published electronically: February 1, 2011
  • Additional Notes: The authors were supported by Mi.U.R. project “Metodi variazionali e topologici nello studio di fenomeni non lineari”.
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 3601-3620
  • MSC (2010): Primary 35B40, 35J20, 35J57
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05221-9
  • MathSciNet review: 2775820