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Global bifurcation and a theorem of Tarantello. (English) Zbl 0797.34021
The authors investigate the number of solutions (and their zeros) of the fourth order boundary value problem \(u''''+ cu''= b[(u+ 1)^ +-1]\), \(u(0)= u''(0)= u(r)= u''(r)=0\). To prove their main result, the authors use the method of global bifurcation due to Rabinowitz and the nodal properties of solutions of a second order boundary value problem.

34B15 Nonlinear boundary value problems for ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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