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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 $\left (p,2\right )$-equations
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by Sergiu Aizicovici, Nikolaos S. Papageorgiou and Vasile Staicu PDF
Trans. Amer. Math. Soc. 367 (2015), 7343-7372 Request permission

Abstract:

In this paper, we study a nonlinear elliptic equation driven by the sum of a $p$-Laplacian and a Laplacian ($\left ( p,2\right )$-equation), with a Carathéodory $\left ( p-1\right )$-(sub-)linear reaction. Using variational methods combined with Morse theory, we prove two multiplicity theorems providing precise sign information for all the solutions (constant sign and nodal solutions). In the process, we prove two auxiliary results of independent interest.
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Additional Information
  • Sergiu Aizicovici
  • Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
  • Email: aizicovs@ohio.edu
  • Nikolaos S. Papageorgiou
  • Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
  • MR Author ID: 135890
  • Email: npapg@math.ntua.gr
  • Vasile Staicu
  • Affiliation: Department of Mathematics, CIDMA, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
  • Email: vasile@ua.pt
  • Received by editor(s): February 22, 2013
  • Received by editor(s) in revised form: November 7, 2013
  • Published electronically: October 21, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 7343-7372
  • MSC (2010): Primary 35J20, 35J60, 35J92, 58E05
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06324-1
  • MathSciNet review: 3378832