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Nodal solutions for $ (p,2)$-equations


Authors: Sergiu Aizicovici, Nikolaos S. Papageorgiou and Vasile Staicu
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
Published electronically: October 21, 2014
MathSciNet review: 3378832
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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
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

DOI: https://doi.org/10.1090/S0002-9947-2014-06324-1
Keywords: Nodal and constant sign solutions, critical groups, strong comparison principle, critical point of mountain pass type, Shifting theorem, Morse relation, local minimizers.
Received by editor(s): February 22, 2013
Received by editor(s) in revised form: November 7, 2013
Published electronically: October 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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