Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T04:55:40.056Z Has data issue: false hasContentIssue false
  • English
  • Français

Bifurcations of second order problems with jumping nonlinearities

Published online by Cambridge University Press:  17 April 2009

Pavel Drábek  and
Milan Kučera
Pavel Drábek
Affiliation:
KMA VŠSE, Nejedleho Sady 14, 306 14 Plzen, Czechoslovakia
Milan Kučera
Affiliation:
MU CSAVZitna 2511567 PrahaCzechoslovakia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we deal with nonlinear second order boundary value problems for ordinary differential equations including the case of jumping nonlinearities. The set of generalised eigenvalues in the case of nonconstant coefficients is described. It is proved that these generalised eigenvalues are simultaneously bifurcation points of the problem with coefficients also depending on the solution u = u(x).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 2 , April 1988 , pp. 179 - 187
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Boccardo, L., ‘Positive eigenfunctions for a class of quasilinear operators’, Boll. Un. Mat. Ital. 5 (1981), 951–959.Google Scholar
[2]Dancer, E.N., ‘On a nonlinear elliptic boundary-value problem’, Bull. Austral. Math. Soc. 12 (1975), 399–405.CrossRefGoogle Scholar
[3]Dancer, E.N., ‘Boundary value problems for weakly nonlinear ordinary differential equations’, Bull. Austral. Math. Soc. 15 (1976), 321–328.Google Scholar
[4]Fucík, S., Solvability of Nonlinear Equations and Boundary Value Problems (D. Reidel Publ Comp., Dordrecht, 1980).Google Scholar
[5]Kamke, E., Differential Gleichungen, Lösungs-methoden und Lösungen, Russian (Nauka, Moscow, 1971).Google Scholar