\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Imperfect bifurcations via topological methods in superlinear indefinite problems

Abstract Related Papers Cited by
  • In [5] the structure of the bifurcation diagrams of a class of superlinear indefinite problems with a symmetric weight was ascertained, showing that they consist of a primary branch and secondary loops bifurcating from it. In [4] it has been proved that, when the weight is asymmetric, the bifurcation diagrams are no longer connected since parts of the primary branch and loops of the symmetric case form an arbitrarily high number of isolas. In this work we give a deeper insight on this phenomenon, studying how the secondary bifurcations break as the weight is perturbed from the symmetric situation. Our proofs rely on the approach of [5,4], i.e. on the construction of certain Poincaré maps and the study of how they vary as some of the parameters of the problems change, obtaining in this way the bifurcation diagrams.
    Mathematics Subject Classification: 34B15, 34C23, 35B30.

    Citation:

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

    M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal., 8 (1971) 321-340.

    [2]

    P. Liu, J. Shi and Y. Wang, Imperfect transcritical and pitchfork bifurcations, J. Funct. Anal., 251 (2007), 573-600.

    [3]

    J. López-Gómez, M. Molina-Meyer and A. Tellini, Intricate bifurcation diagrams for a class of one-dimensional superlinear indefinite problems of interest in population dynamics, DCDS Supplement 2013 Proceedings of the 9th AIMS International Conference, 515-524.

    [4]

    J. López-Gómez and A. Tellini, Generating an arbitrarily large number of isolas in a superlinear indefinite problem, Nonlinear Anal. - Theory Methods Appl., 108 (2014), 223-248.

    [5]

    J. López-Gómez, A. Tellini and F. Zanolin, High multiplicity and complexity of the bifurcation diagrams of large solutions for a class of superlinear indefinite problems, Commun. Pure Appl. Anal., 13 (2014), 1-73.

  • 加载中
Open Access Under a Creative Commons license
SHARE

Article Metrics

HTML views() PDF downloads(125) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return