scholarly journals Analytical solution of a class of nonlinear differential equations of the third order in the complex area

2021 ◽  
pp. 75-84
Author(s):  
Виктор Николаевич Орлов ◽  
Людмила Витальевна Мустафина
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Third Order ◽  
The Third ◽  
Change Of Variables ◽  
Priori Estimates

В работе приводится доказательство теоремы существования и единственности аналитического решения класса нелинейных дифференциальных уравнений третьего порядка, правая часть которого представлена полиномом шестой степени, в комплексной области. Расширен класс рассматриваемых уравнений за счет новой замены переменных. Получена априорная оценка аналитического приближенного решения. Представлен вариант численного эксперимента оптимизации априорных оценок с помощью апостериорных. The article presents a proof of the theorem of the existence and uniqueness of the analytical solution of the class of nonlinear differential equations of the third order, with a polynomial right-hand side of the sixth degree, in the complex domain. The class of the considered equations has been extended by means of a new change of variables. An a priori estimate of the analytical approximate solution is obtained. A variant of the numerical experiment of optimizing a priori estimates using a posteriori estimates is presented.

scholarly journals Existence theorem for a solution of a class of third order nonlinear differential equations with polynomial right hand side of the seventh degree in a vicinity of a movable singular point

2020 ◽  
pp. 92-100
Author(s):  
Виктор Николаевич Орлов ◽  
Магомедюсуф Владимирович Гасанов
Keyword(s):  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
A Posteriori ◽  
Existence And Uniqueness Theorem ◽  
Third Order ◽  
Priori Estimates ◽  
A Priori Estimation ◽  
Posteriori Estimation

В настоящей статье дано развитие варианта доказательства теоремы существования и единственности решения рассматриваемого класса нелинейных дифференциальных уравнений, характерной особенностью которых является наличие подвижных особых точек. Представленное доказательство позволяет построить аналитическое приближенное решение, получить его априорные оценки. Апостериорная оценка позволяет оптимизировать априорную оценку. Теоретический материал протестирован с помощью численного эксперимента. This article gives the development of a version of the proof of the existence and uniqueness theorem for the solution of the class of nonlinear differential equations under consideration whose characteristic feature is the presence of movable singular points. The presented proof allows us to construct an analytical approximate solution and obtain its a priori estimates. A posteriori estimation allows to optimize a priori estimation. The theoretical material is tested using a numerical experiment.

Numerical analysis of nonlinear model of excited carrier decay

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Natalija Tumanova ◽  
Raimondas Čiegis ◽  
Mečislavas Meilūnas
Keyword(s):  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Euler Method ◽  
Genetic Optimization ◽  
Identifiability Analysis ◽  
Priori Estimates ◽  
Backward Euler ◽  
Excited Carrier

AbstractThis paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.

scholarly journals Solvability of a Third-Order Singular Generalized Left Focal Problem in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-18
Author(s):  
Youwei Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Multiple Positive Solutions ◽  
Third Order ◽  
The Third ◽  
Priori Estimates

We consider the existence of positive solution for a third-order singular generalized left focal boundary value problem with full derivatives in Banach spaces. Green’s function and its properties, explicit a priori, estimates will be presented. By means of the theories of the fixed point in cones, we establish some new and general results on the existence of single and multiple positive solutions to the third-order singular generalized left focal boundary value problem. Our results are generalizations and extensions of the results of the focal boundary value problem. An example is included to illustrate the results obtained.

scholarly journals An approximate solution of the one class third order onlinear differential equation in the analyticity domain

2020 ◽  
pp. 45-54
Author(s):  
Виктор Николаевич Орлов ◽  
Рио-Рита Вадимовна Разакова
Keyword(s):  
Approximate Solution ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Existence And Uniqueness Theorem ◽  
Third Order ◽  
Analyticity Domain ◽  
Priori Estimates ◽  
The One

В работе рассмотрен класс нелинейных дифференциальных уравнений третьего порядка с полиномиальной правой частью шестой степени. Доказана теорема существования и единственности решения в области аналитичности. Построено аналитическое приближенное решение. Предложен вариант оптимизации априорных оценок с помощью апостериорных. Проведен численный эксперимент. There is a class of third-order nonlinear differential equations with polynomial right part of the sixth degree considered in the paper. The existence and uniqueness theorem of a solution in the domain of analyticity is proved by authors. There is an analytical approximate solution which was constructed by V. Orlov and R. Razakova. A variant of optimization of a priori estimates using posterior ones is proposed by authors. A numerical experiment is carried out too.

scholarly journals A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said Mesloub ◽  
Hassan Eltayeb Gadain
Keyword(s):  
Differential Equations ◽  
Evolution Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
A Priori Bounds ◽  
Fractional Evolution Equation ◽  
Priori Estimates ◽  
Initial Boundary Value

Abstract A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

scholarly journals Positive solutions of higher order quasilinear elliptic equations

2002 ◽  
Vol 7 (8) ◽  
pp. 423-452
Author(s):  
Marcelo Montenegro
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
A Priori Estimate ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
The Maximum Principle ◽  
Priori Estimates ◽  
Quasilinear Elliptic

The higher order quasilinear elliptic equation−Δ(Δp(Δu))=f(x,u)subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also presented. The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel'skiĭ fixed point theorem.

scholarly journals Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections

2020 ◽  
Author(s):  
Hanwu Li ◽  
Yongsheng Song
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Backward Stochastic Differential Equations ◽  
Penalization Method ◽  
Priori Estimates ◽  
Uniqueness And Existence

Abstract In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the solution lies between two prescribed processes. A new kind of approximate Skorohod condition is proposed to derive the uniqueness and existence of the solutions. The uniqueness can be proved by a priori estimates and the existence is obtained via a penalization method.

On solutions of third order nonlinear differential equations

2006 ◽  
Vol 4 (1) ◽  
pp. 46-63 ◽  
Author(s):  
Ivan Mojsej ◽  
Ján Ohriska
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Property A ◽  
Comparison Result ◽  
Third Order ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
The Third

AbstractThe aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.

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