Open AccessHigh multiplicity and complexity of the bifurcation diagrams of large solutions for a class of superlinear indefinite problems
Author(s) -
Julián López-Góme,
Andrea Tellini,
Fabio Zanolin
Publication year - 2014
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2014.13.1
Subject(s) - multiplicity (mathematics) , mathematics , bifurcation diagram , bifurcation , homogeneous , mathematical analysis , class (philosophy) , diagram , boundary value problem , simple (philosophy) , pure mathematics , term (time) , nonlinear system , physics , combinatorics , computer science , quantum mechanics , artificial intelligence , philosophy , statistics , epistemology
This paper analyzes the existence and structure of the positive solutions of a very simple superlinear indefinite semilinear elliptic prototype model under non-homogeneous boundary conditions, measured by M ≤ ∞. Rather strikingly, there are ranges of values of the parameters involved in its setting for which the model admits an arbitrarily large number of positive solutions, as a result of their fast oscillatory behavior, for sufficiently large M. Further, using the amplitude of the superlinear term as the main bifurcation parameter, we can ascertain the global bifurcation diagram of the positive solutions. This seems to be the first work where these multiplicity results have been documented