Abstract
We study the existence of positive solutions of the nonlinear boundary value problem u ( 4 ) ( t ) = f ( t , u ( t ) , u ″ ( t ) ) , t ∈ ( 0 , 1 ) , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , which is not necessarily linearizable. Our approaches are based on Krein–Rutman theorem, topological degree theory and global bifurcation techniques.
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