Przybycin, Jolanta Some applications of bifurcation theory to ordinary differential equations of the fourth order. (English) Zbl 0729.34022 Ann. Pol. Math. 53, No. 2, 153-160 (1991). 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. Reviewer: P.N.Bajaj (Wichita) Cited in 4 Documents MSC: 34C23 Bifurcation theory for ordinary differential equations 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators Keywords:nonlinear eigenvalue problems; fourth order differential equations; results of Rabinowitz; bifurcation PDFBibTeX XMLCite \textit{J. Przybycin}, Ann. Pol. Math. 53, No. 2, 153--160 (1991; Zbl 0729.34022) Full Text: DOI