Search results for "Differential equation"
showing 10 items of 759 documents
Indefinite integrals of special functions from integrating factors
2019
Some general integrals are presented which were obtained from two integrating factors f(x) and fˆ(x) for the first two and last two terms, respectively, of the second-order linear ordinary differen...
Singular integrals and rectifiability
2002
We shall discuss singular integrals on lower dimensional subsets of Rn. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey of some newer results and open problems. In the second part we prove some results on the Riesz kernels in Rn. As far as I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
A probabilistic Weitzenböck formula on Riemannian path space
2000
Generalizations of Clausen's formula and algebraic transformations of Calabi-Yau differential equations
2011
AbstractWe provide certain unusual generalizations of Clausen's and Orr's theorems for solutions of fourth-order and fifth-order generalized hypergeometric equations. As an application, we present several examples of algebraic transformations of Calabi–Yau differential equations.
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular freq…
1995
If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper. In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II. Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as—if the equations are viewed as a three-dimensional dynamical system—the unique stable equilibrium, which depends on the spin. This equilibri…
Local regularity for quasi-linear parabolic equations in non-divergence form
2018
Abstract We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p -Laplacian type and in non-divergence form. We provide local Holder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Holder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.
Oscillation criteria for even-order neutral differential equations
2016
Abstract We study oscillatory behavior of solutions to a class of even-order neutral differential equations relating oscillation of higher-order equations to that of a pair of associated first-order delay differential equations. As illustrated with two examples in the final part of the paper, our criteria improve a number of related results reported in the literature.
On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations
2016
In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.
Modelling the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia: an epidemiological approach with unc…
2013
Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students academic performance in the German region of North Rhine-Westphalia. This approach is supported by the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years.