Morse theory methods for a class of quasi-linear elliptic systems of higher order

  • Guangcun LuEmail author


We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll–Meyer’s splitting theorem and a weaker Marino–Prodi perturbation type result. They are applicable to a wide range of multiple integrals with quasi-linear elliptic Euler equations and systems of higher order.

Mathematics Subject Classification

Primary 58E05 49J52 49J45 



The author is grateful to the anonymous referees for useful remarks.


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Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems, School of Mathematical SciencesBeijing Normal University, Ministry of EducationBeijingThe People’s Republic of China

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