Variational Methods and Nonlinear Problems: Classical Results and Recent Advances

  • Antonio Ambrosetti
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 15)


Around the end of the Twenties two memoires, a first one by Morse [63] and a second one by Lusternik and Schnirelman [59], marked the birth of those variational methods known under the name of Calculus of Variation in the Large. These tools are mainly concerned with the existence of critical points, distinct from minima, which give rise to solutions of nonlinear differential equations. The elegance of the abstract tools and the broad range of applications to problems that had been considered of formidable difficulty, such as the existence of closed geodesics on a compact anifold or the problem of minimal surfaces, have rapidly made the Calculus of Variation in the Large a very fruitful field of research.


Periodic Solution Weak Solution Hamiltonian System Morse Index Critical Point Theory 
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© Birkhäuser Boston 1995

Authors and Affiliations

  • Antonio Ambrosetti
    • 1
  1. 1.Scuola Normale SuperiorePisaItaly

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