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

Ruyun Ma, Yulian 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.

Gradient systems of closed operators

Vittorino Pata (2009)

Open Mathematics

A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.

Green-Liouville approximation and correct solvability in L p ( ) of the general Sturm-Liouville equation

Nina Chernyavskaya, Leonid Shuster (2024)

Czechoslovak Mathematical Journal

We consider the equation - ( r ( x ) y ' ( x ) ) ' + q ( x ) y ( x ) = f ( x ) , x , where f L p ( ) , p ( 1 , ) and r > 0 , 1 r L 1 loc ( ) , q L 1 loc ( ) . For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions r and q under which the above equation is correctly solvable in the space L p ( ) , p ( 1 ...

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