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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...

Mathematical analysis of the optimizing acquisition and retention over time problem

Adi Ditkowski (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

Adi Ditkowski (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

Mathematical model for the basilar membrane as a two dimensional plate.

Alkahby, H.Y., Mahrous, M.A., Mamo, B. (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Maximum principle and its extension for bounded control problems with boundary conditions.

Vasilieva, Olga (2004)

International Journal of Mathematics and Mathematical Sciences

Maximum principles and uniqueness results of phi-Laplacian boundary value problems.

Heikkilä, S., Seikkala, S. (2001)

Journal of Inequalities and Applications [electronic only]

Maximum principles for a family of nonlocal boundary value problems.

Eloe, Paul W. (2004)

Advances in Difference Equations [electronic only]

Mesh Selection for Discrete Solution of Boundary Problems in Ordinary Differential Equations.

V. Pereyra, E.G. Sewell (1974/1975)

Numerische Mathematik

Method of lower and upper solutions for a generalized boundary value problem

Boris Rudolf (2000)

Archivum Mathematicum

Method of lower and upper solutions for a third-order three-point regular boundary value problem

Martin Šenkyřík (1992)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Method of successive approximations for a certain nonlinear third order boundary value problem

Ján Rusnák (1987)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Method of the quasilinearization for nonlinear impulsive differential equations with linear boundary conditions.

Eloe, P., Hristova, S.G. (2002)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Methods of analysis of the condition for correct solvability in $L_{p} (ℝ)$ of general Sturm-Liouville equations

Nina A. Chernyavskaya, Leonid A. Shuster (2014)

Czechoslovak Mathematical Journal

We consider the equation $- {(r (x) y^{'} (x))}^{'} + q (x) y (x) = f (x), x \in ℝ (*)$ where $f \in L_{p} (ℝ)$ , $p \in (1, \infty)$ and $\begin{matrix} r > 0, q \geq 0, \frac{1}{r} \in L_{1}^{loc} (ℝ), q \in L_{1}^{loc} (ℝ), \\ lim_{| d | \to \infty} \int_{x - d}^{x} \frac{d t}{r (t)} \cdot \int_{x - d}^{x} q (t) d t = \infty . \end{matrix}$ In an earlier paper, we obtained a criterion for correct solvability of ( $*$ ) in $L_{p} (ℝ),$ $p \in (1, \infty) ...$

Metoda přesunu okrajových podmínek

Emil Vitásek (2007)

Pokroky matematiky, fyziky a astronomie

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