Bifurcation in nonlinearizable eigenvalue problems for ordinary differential equations of fourth order with indefinite weight

Abstract

We consider a nonlinearizable eigenvalue problem for the beam equation with an indefinite weight function. We investigate the structure of bifurcation set and study the behavior of connected components of the solution set bifurcating from the line of trivial solutions and contained in the classes of positive and negative functions.

Keywords

• nonlinear eigenvalue problem
• bifurcation point
• principal eigenvalues
• global continua
• indefinite weight