Mathematical Sciences
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SturmLiouville Equations with Singular Endpoints of Poincaré Rank Zero and One
(201705)In this dissertation, my objective is to study, for x ∊ (0, ∞), the equations (1) (xy′)′ + (‐v²/x + λ x)y = 0, with a view to obtaining representations of solutions near the singular endpoints, connection formulas for ... 
Set differential equations with causal operators
(20050428)We obtain some basic results on existence, uniqueness, and continuous dependence of solutions with respect to initial values for set differential equations with causal operators. 
Optimality Conditions for Systems Driven by Nonlinear Evolution Equations
(1995)Using the DubovitskiiMilyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or ... 
Discrete Riccati Equation Solutions: Distributed Algorithms
(1996)In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. ... 
On the Structure of the Deflagration for the Generalized ReactionRate Model
(1996)The structure of the deflagration is examined by means of an asymptotic analysis of the physicalplane boundaryvalue problem, with LewisSemenov number unity, in the limit of the activationtemperature ratio, β = Ta/Tb, ... 
Two (Multi) Point Nonlinear Lyapunov Systems Associated with an nth Order Nonlinear System of Differential Equations  Existence and Uniqueness
(2000)This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an nth order nonlinear Lyapunov system. A variation of parameters formula is ... 
Asymptotic Analysis of the Structure of a Steady Planar Detonation: Review and Extension
(1999)The structure of a steady planar ChapmanJouguet detonation, which is supported by a direct firstorder onestep irreversible exothermic unimolecular reaction, subject to Arrhenius kinetics, is examined. Solutions are ... 
The hypersonic NavierStokes approximation for the normal shock structure of a perfect gas with the Sutherland viscosity law: Review and extension
(1998)By means of a fourregion asymptotic analysis, a uniformly valid description of the Sutherlandviscositylaw NavierStokes structure of the normal shock wave in the hypersonic approximation is obtained. 
An upper and lower solution approach for a generalized Thomas–Fermi theory of neutral atoms
(200204)An upper and lower solution theory for boundary value problems modeled from the ThomasFermi equation, was presented. The approach was subjected to a boundary condition corresponding to the neutral atom with Bohr radius. ... 
Uniqueness Criterion for Solution of Abstract Nonlocal Cauchy Problem
(1993)The aim of the paper is to prove an uniqueness criterion for a solution of an abstract nonlocal Cauchy problem. A dissipative operator in the nonlocal problem and an arbitrary functional in the nonlocal condition are ... 
Quasilinearization for Some Nonlocal Problems
(1993)The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation ut – Lu = f{t,x,u) with nonlocal boundary conditions u(t,x)=∫Ωϕ(x,y)u(t,y)dy in this paper. The convexity of f in u is ... 
Optimal Controllability of Impulsive Control Systems
(1993)The problem of optimal controllability of a nonlinear impulsive control system is studied using the method of vector Lyapunov functions and the generalized comparison principle. 
Converge, Version 3.0 Software for Algebra Through Calculus A Software Review
(1993)Although intended for college teachers/students, Converge presents a feature that may interest all scientists: it allows an easy export of graphic files to most known word processors, specifically to the EXP, Version 2.1, ... 
On the structure of a distinguishedlimit quasiisothermal deflagration for the generalized reactionrate model
(1997)The structure of the quasiisothermal deflagration is examined by means of an asymptotic analysis of the physicalplane boundaryvalue problem, with LewisSemenov number unity, in the limit of the activationtemperature ... 
Existence Criteria for Singular Initial Value Problems with Sign Changing Nonlinearities
(2001)A general existence theory is presented for initial value problems where our nonlinearity may be singular in its dependent variable and may also change sign. 
Variational Lyapunov method and stability theory
(1998)By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing ... 
Stability of Conditionally Invariant Sets and Controlled Uncertain Dynamic Systems on Time Scales
(1995)A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected ... 
Boundary value problems on the half line in the theory of colloids
(200204)We present existence results for some boundary value problems defined on infinite intervals. In particular our discussion includes a problem which arises in the theory of colloids. 
Random fixed point theory in spaces with two metrics
(2003)We present new random fixed point theorems in spaces with two metrics. Our results extend recent results of Tan and Yuan [10] and Xu [11].