Advanced Search
Article Contents
Article Contents

A global implicit function theorem and its applications to functional equations

Abstract Related Papers Cited by
  • The main result of the paper is a global implicit function theorem. In the proof of this theorem, we use a variational approach and apply Mountain Pass Theorem. An assumption guarantying existence of an implicit function on the whole space is a Palais-Smale condition. Some applications to differential and integro-differential equations are given.
    Mathematics Subject Classification: Primary: 26B10, 47J07.


    \begin{equation} \\ \end{equation}
  • [1]

    A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381.doi: 10.1016/0022-1236(73)90051-7.


    M. Cristea, A note on global implicit function theorem, J. Inequal. Pure and Appl., 8 (2007), 15 pp.


    D. Idczak, A. Skowron and S. Walczak, On the diffeomorphisms between Banach and Hilbert spaces, Advanced Nonlinear Studies, 12 (2012), 89-100.


    A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems, North-Holland, 1979.


    P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Amer. Math. Soc., Providence, 1986.


    W. C. Rheinboldt, Local mapping relations and global implicit function theorems, Trans. Amer. Math. Soc., 138 (1969), 183-198.doi: 10.1090/S0002-9947-1969-0240644-0.


    M. Willem, Minimax Theorems, Birkhauser, Boston, 1996.doi: 10.1007/978-1-4612-4146-1.


    W. Zhang and S. S. Ge, A Global Implicit Function Theorem without initial point and its applications to control of non-affine systems of high dimensions, J. Math. Anal. Appl, 313 (2006), 251-261.doi: 10.1016/j.jmaa.2005.08.072.

  • 加载中

Article Metrics

HTML views() PDF downloads(743) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint