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On a singular multi-point third-order boundary value problem on the half-line

Zakia Benbaziz, Smail Djebali (2020)

Mathematica Bohemica

We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel’skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity f = f ( t , x , y ) which satisfies upper and lower-homogeneity conditions in the space variables x , y may be also singular at time t = 0 . Two examples of applications...

On a stochastic SIR model

Elisabetta Tornatore, Stefania Maria Buccellato (2007)

Applicationes Mathematicae

We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.

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