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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 27, Issue 3


On a class of parametric Neumann problems with indefinite and unbounded potential

Nikolaos S. Papageorgiou / George Smyrlis
Published Online: 2013-06-28 | DOI: https://doi.org/10.1515/forum-2012-0042


We consider a parametric Neumann problem with an indefinite and unbounded potential. Using a combination of critical point theory with truncation and comparison techniques, with Morse theory and with invariance arguments for a suitable negative gradient flow, we prove two multiplicity theorems for certain values of the parameter. In the first theorem we produce three solutions and in the second five. For all solutions we provide sign information. Our work improves significantly results existing in the literature.

Keywords: Indefinite and unbounded potential; truncations-perturbations; mountain pass theorem; Morse theory; gradient flow; invariance properties

MSC: 35J20; 35J60; 58E05

About the article

Received: 2012-03-31

Revised: 2013-04-07

Published Online: 2013-06-28

Published in Print: 2015-05-01

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1743–1772, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0042.

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