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Some addition to the generalized Riemann-Hilbert problem

R.R. Gontsov, I.V. Vyugin (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the generalized Riemann-Hilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be non-minimal, the problem is known to have a solution. In this article we give a bound for the possibly non-minimal Poincaré rank. We also give a bound for the number of apparent singularities of a scalar equation with prescribed generalized monodromy data.

Some algebraic fixed point theorems for multi-valued mappings with applications

Bupurao C. Dhage (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.

Some classes of linear n th-order differential equations

Valter Šeda (1997)

Archivum Mathematicum

Sufficient conditions for the n -th order linear differential equation are derived which guarantee that its Cauchy function K , together with its derivatives i K t i , i = 1 , , n - 1 , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.

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