On differential systems with strongly indefinite variational structure

By C. J. Batkam, F. Colin, T. Kaczynski. 2014

64 citations recorded by the source corpus.

We obtain multiplicity results for a class of first-order superquadratic Hamiltonian systems and a class of indefinite superquadratic elliptic systems which lead to the study of strongly indefinite functionals. There is no assumption to the effect that the nonlinear terms have to satisfy the Ambrosetti–Rabinowitz superquadratic condition. To establish the existence of solutions, a new version of the symmetric mountain pass theorem for strongly indefinite functionals is presented in this paper. This theorem is subsequently applied to deal with cases where all the Palais–Smale sequences of the energy functional may be unbounded.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bc35e21cc1986ec5fcbf2b7413638d46139d1659

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In Applied Mathematics

1. Denis Bonheure
2. Ederson Moreira dos Santos
3. Hugo Tavares

In Computational Theory and Mathematics

1. Ederson Moreira dos Santos
2. Denis Bonheure
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In Statistical and Nonlinear Physics

1. Ederson Moreira dos Santos
2. Hugo Tavares
3. Denis Bonheure

Citations in the corpus

• Hamiltonian elliptic systems: a guide to variational frameworks (2014, methodology): “However, in [62] the proof is done for the more restrictive case”