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Inverse problems on star-type graphs: differential operators of different orders on different edges

Vyacheslav Yurko (2014)

Open Mathematics

We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

IVPs for singular multi-term fractional differential equations with multiple base points and applications

Yuji Liu, Pinghua Yang (2014)

Applicationes Mathematicae

The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term fractional...

Kamenev type oscillation criteria for second order matrix differential systems with damping

Qi-gui Yang, Sui Sun Cheng (2005)

Annales Polonici Mathematici

By using monotone functionals and positive linear functionals on a suitable matrix space, new oscillation criteria for second order self-adjoint matrix differential systems with damping are given. The results are extensions of the Kamenev type oscillation criteria obtained by Wong for second order self-adjoint matrix differential systems with damping. These extensions also include an earlier result of Erbe et al.

Kinetical systems

Ladislav Adamec (1997)

Applications of Mathematics

The aim of the paper is to give some preliminary information concerning a class of nonlinear differential equations often used in physical chemistry and biology. Such systems are often very large and it is well known that where studying properties of such systems difficulties rapidly increase with their dimension. One way how to get over the difficulties is to use special forms of such systems.

Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (1995)

Annales Polonici Mathematici

We investigate the structure of the set of solutions of the Cauchy problem x’ = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in C w ( I , E ) , the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory solutions,...

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