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Positive solutions for a system of fractional boundary value problems

Henderson, Johnny, Luca, Rodica (2017)

Proceedings of Equadiff 14

We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.

Positive stable realizations of fractional continuous-time linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.

Positively homogeneous functions and the Łojasiewicz gradient inequality

Alain Haraux (2005)

Annales Polonici Mathematici

It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on N satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.

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