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Global structure of positive solutions for superlinear 2 m th-boundary value problems

Ruyun MaYulian An — 2010

Czechoslovak Mathematical Journal

We consider boundary value problems for nonlinear 2 m th-order eigenvalue problem ( - 1 ) m u ( 2 m ) ( t ) = λ a ( t ) f ( u ( t ) ) , 0 < t < 1 , u ( 2 i ) ( 0 ) = u ( 2 i ) ( 1 ) = 0 , i = 0 , 1 , 2 , , m - 1 . where a C ( [ 0 , 1 ] , [ 0 , ) ) and a ( t 0 ) > 0 for some t 0 [ 0 , 1 ] , f C ( [ 0 , ) , [ 0 , ) ) and f ( s ) > 0 for s > 0 , and f 0 = , where f 0 = lim s 0 + f ( s ) / s . We investigate the global structure of positive solutions by using Rabinowitz’s global bifurcation theorem.

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