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Weak and classical positive solutions of some elliptic equations in W, Rn,n≥3; radially symmetric cases

September 1994
The Quarterly Journal of Mathematics 45(179)

DOI:10.1093/qmath/45.3.397

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University of Copenhagen

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On Anisotropic Elliptic Equations in Bounded Domains

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Jan 2004

Tadie Tadie

Because of the anisotropic character of the equations in (Qc) and (Pc) below, in solving those problems, we cannot right away apply the comparison principles. We will pick up some conditions under which the existence of some sub-and-super solutions of the problems leads to the existence theorems for those problems.

Monotonicity and boundedness of the atomic radius in the Thomas-Fermi theory

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Jan 1999
Can Appl Math Q

Tadie Tadie

Following the Thomas-Fermi theory for atoms, we provide a mathematical proof of the fact that atoms grow in size with bounded radii as one goes down each group in the periodic table. The boundedness of the radii is quite known from experiments, but the fact that they are monotone increasing has not been established although it has been predicted for some time.

ResearchGate has not been able to resolve any references for this publication.

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Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with lo...

March 2011 · ESAIM Proceedings

Gerardo Rubio

We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. ... [Show full abstract] The linear equations involved can not be solved with the traditional results. Therefore, we construct a classical solution to the linear Cauchy problem under the same hypotheses on the coefficients for the semilinear equation. Our approach is using stochastic differential equations and parabolic differential equations in bounded domains. Finally, we apply the results to a stochastic optimal consumption problem.

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On the relation between the continuous and discrete Painlevé equations

April 2012 · Theoretical and Mathematical Physics

A method for deriving difference equations (the discrete Painlevé equations in particular) from the Bäcklund transformations of the continuous Painlevé equations is discussed. This technique can be used to derive several of the known discrete painlevé equations (in particular, the first and second discrete Painlevé equations and some of their alternative versions). The Painlevé equations possess ... [Show full abstract] hierarchies of rational solutions and one-parameter families of solutions expressible in terms of the classical special functions for special values of the parameters. Hence, the aforementioned relations can be used to generate hierarchies of exact solutions for the associated discrete Painlevé equations. Exact solutions of the Painlevé equations simultaneously satisfy both a differential equation and a difference equation, analogously to the special functions.

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Weighted pseudo-almost periodic solutions to some differential equations

April 2008 · Nonlinear Analysis

Toka Diagana

The paper considers some new classes of functions called weighted pseudo-almost periodic functions, which implement in a natural fashion the classical pseudo-almost periodic functions due to Zhang. Properties of these weighted pseudo-almost periodic functions are discussed, including a composition result for weighted pseudo-almost periodic functions. The results obtained are subsequently utilized ... [Show full abstract] to study the existence and uniqueness of a weighted pseudo-almost periodic solution to the heat equation with Dirichlet conditions.

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A second-order smooth penalty function algorithm for constrained optimization problems

May 2013 · Computational Optimization and Applications

This paper introduces a second-order differentiability smoothing technique to the classical l 1 exact penalty function for constrained optimization problems(COP). Error estimations among the optimal objective values of the nonsmooth penalty problem, the smoothed penalty problem and the original optimization problem are obtained. Based on the smoothed problem, an algorithm for solving COP is ... [Show full abstract] proposed and some preliminary numerical results indicate that the algorithm is quite promising.

Last Updated: 22 Oct 2024