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Linearized comparison criteria for a nonlinear neutral differential equation

Xinping Guan, Sui Sun Cheng (1996)

Annales Polonici Mathematici

A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.

Local Bifurcations in a Nonlinear Model of a Bioreactor

Dimitrova, Neli (2009)

Serdica Journal of Computing

This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008.We consider a nonlinear model of a continuously stirred bioreactor and study the stability of the equilibrium points with respect to practically important model parameters. We determine regions in the parameter space where the steady states undergo transcritical and Hopf bifurcations. In the latter case, the stability of the emerged limit cycles is also studied. Numerical simulations in the computer algebra...

Lyapunov type inequalities for a second order differential equation with a damping term

S. H. Saker (2012)

Annales Polonici Mathematici

For a second order differential equation with a damping term, we establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivative. We also obtain a lower bound for the first eigenvalue of a boundary value problem. The main results are proved by applying the Hölder inequality and some generalizations of Opial and Wirtinger type...

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