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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.

MSC:
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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