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Some applications of bifurcation theory to ordinary differential equations of the fourth order. (English) Zbl 0729.34022

The purpose of this paper is to study nonlinear eigenvalue problems for some fourth order differential equations. These equations are converted into equivalent integral ones, and, then, the results of Rabinowitz are applied. The main theorem connected with bifurcation from the line of trivial solutions is proved in Section 1. A related theorem for bifurcation from infinity is proved in Section 2.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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