Liouvillian first integrals of second order polynomial differential equations.
Ljusternik-Schnirelman theory with local Palais-Smale condition and singular dynamical systems
Local Bifurcations in a Nonlinear Model of a Bioreactor
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...
Local integrating factors.
Local invariance via comparison functions.
Local method of nonlinear analysis
Local models of the greatest characteristic exponent of differential equations depending on parameters
Localization of periodic orbits of autonomous systems based on high-order extremum conditions.
Logarithmic derivatives of solutions of disconjugate differential equations
Long term behavior of solutions for Riccati initial-value problems.
Lower and upper bounds for the splitting of separatrices of a pendulum under a fast quasiperiodic forcing.
Lp-Perturbations of Second Order Linear Differential Equations.
Lyapunov type inequalities for a second order differential equation with a damping term
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...
Lyapunov type integral inequalities for certain differential equations.
Lyapunov-type inequality for higher-order differential equations
Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques
Majorization of -semigroups in ordered Banach spaces
We give criteria for domination of strongly continuous semigroups in ordered Banach spaces that are not necessarily lattices, and thus obtain generalizations of certain results known in the lattice case. We give applications to semigroups generated by differential operators in function spaces which are not lattices.
Maslov index for homoclinic orbits of hamiltonian systems
Mathematical analysis of the optimizing acquisition and retention over time problem
While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...
Mathematical analysis of the optimizing acquisition and retention over time problem
While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...