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Existence of one-signed solutions of nonlinear four-point boundary value problems

Ruyun Ma, Ruipeng Chen (2012)

Czechoslovak Mathematical Journal

In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems - u ' ' + M u = r g ( t ) f ( u ) , u ( 0 ) = u ( ε ) , u ( 1 ) = u ( 1 - ε ) and u ' ' + M u = r g ( t ) f ( u ) , u ( 0 ) = u ( ε ) , u ( 1 ) = u ( 1 - ε ) , where ε ( 0 , 1 / 2 ) , M ( 0 , ) is a constant and r > 0 is a parameter, g C ( [ 0 , 1 ] , ( 0 , + ) ) , f C ( , ) with s f ( s ) > 0 for s 0 . The proof of the main results is based upon bifurcation techniques.

Existence of positive periodic solutions of an SEIR model with periodic coefficients

Tailei Zhang, Junli Liu, Zhidong Teng (2012)

Applications of Mathematics

An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.

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