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Solvability of a forced autonomous Duffing's equation with periodic boundary conditions in the presence of damping

Chaitan P. Gupta (1993)

Applications of Mathematics

Let g : 𝐑 → 𝐑 be a continuous function, e : [ 0 , 1 ] → 𝐑 a function in L 2 [ 0 , 1 ] and let c ∈ 𝐑 , c ≠ 0 be given. It is proved that Duffing’s equation u ' ' + c u ' + g ( u ) = e ( x ) , 0 < x < 1 , u ( 0 ) = u ( 1 ) , u ' ( 0 ) = u ' ( 1 ) in the presence of the damping term has at least one solution provided there exists an 𝐑 > 0 such that g ( u ) u ≥ 0 for | u | ≥ 𝐑 and ∫ 0 1 e ( x ) d x = 0 . It is further proved that if g is strictly increasing on 𝐑 with lim u → - ∞ g ( u ) = - ∞ , lim u → ∞ g ( u ) = ∞ and it Lipschitz continuous with Lipschitz constant α < 4 π 2 + c 2 , then Duffing’s equation given above has exactly one solution for every e ∈ L 2 [ 0 , 1 ] .

Stability, Boundedness and Existenceof Periodic Solutions to Certain Third Order Nonlinear Differential Equations

A. T. ADEMOLA, M. O. OGUNDIRAN, P. O. ARAWOMO (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, criteria are established for uniform stability, uniform ultimate boundedness and existence of periodic solutions for third order nonlinear ordinary differential equations. In the investigation Lyapunov’s second method is used by constructing a complete Lyapunov function to obtain our results. The results obtained in this investigation complement and extend many existing results in the literature.

Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

T. Dhirasakdanon, H. R. Thieme (2010)

Mathematical Modelling of Natural Phenomena

For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...

Strategies for computation of Lyapunov exponents estimates from discrete data

Fischer, Cyril, Náprstek, Jiří (2019)

Programs and Algorithms of Numerical Mathematics

The Lyapunov exponents (LE) provide a simple numerical measure of the sensitive dependence of the dynamical system on initial conditions. The positive LE in dissipative systems is often regarded as an indicator of the occurrence of deterministic chaos. However, the values of LE can also help to assess stability of particular solution branches of dynamical systems. The contribution brings a short review of two methods for estimation of the largest LE from discrete data series. Two methods are analysed...

Subgroups of odd depth—a necessary condition

Sebastian Burciu (2013)

Czechoslovak Mathematical Journal

This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with { 0 , 1 } -entries to have maximal rank. The entries of the matrix...

Currently displaying 481 – 500 of 587