Charles Stuart

D'origine britannique, Charles Alexander Stuart est né à Newmachar (Ecosse) le 5 juin 1945. Il étudie les mathématiques à l'Université d'Aberdeen, où il obtient une licence (B.Sc.) en 1967, et à Oxford, où il a fait son doctorat (D.Phil) en 1970.

De 1970 à 1974, il est lecteur au Département de mathématiques de l'Université du Sussex. Un congé lui permet de passer deux ans (1973-1975) à Genève, comme chercheur à l'Institut Battelle. Pendant l'année académique 1975-1976, il est lecteur à l'Université d'Aberdeen. Il est nommé professeur extraordinaire à l'EPFL en 1975 et professeur ordinaire en 1982.

Il donne des cours d'analyse à plusieurs sections d'ingénieurs (1er cycle). Pour les 2e et 3e cycles, il traite les équations différentielles et l'analyse fonctionnelle. Ses recherches portent sur les mêmes branches; elles concernent surtout des problèmes de bifurcation qui se présentent dans la modélisation de phénomènes physiques.

Il a passé un premier congé sabbatique (1982-1983) à l'Université de Heriot-Watt et un deuxième (1989-1990) à l'Université Cornell, aux Etats-Unis

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Schrödinger equation

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantu

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as

Derivative

In mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the p

Global bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

Consider F is an element of C(RxX,Y) such that F(lambda, 0) = 0 for all lambda is an element of R, where X and Y are Banach spaces. Bifurcation from the line Rx{0} of trivial solutions is investigated in cases where F(lambda, center dot ) need not be Frechet differentiable at 0. The main results provide sufficient conditions for mu to be a bifurcation point and yield global information about the connected component of {(lambda,u):F(lambda,u)=0 and u not equal 0}?{(mu,0)} containing (mu, 0). Some necessary conditions for bifurcation are also formulated. The abstract results are used to treat several singular boundary value problems for which Frechet differentiability is not available. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.

2021

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Charles Stuart

In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega) u(2) + Sigma(N)(i,j=1) A(ij)partial derivative(j)u partial derivative(i)u dx < infinity and u = 0 on partial derivative Omega, where V is an element of L-infinity(Omega) and the nonlinear terms n and g are of higher order near 0 so that the formal linearization about the trivial solution u 0 is - Sigma(N)(i,j=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + Vu = lambda u. The leading term is degenerate elliptic on Omega because it is assumed that there are constants C-2 >= C-1 > 0 such that C1 vertical bar x vertical bar(2)vertical bar xi vertical bar(2)

2020

Qualitative properties and global bifurcation of solutions for a singular boundary value problem

Charles Stuart

This paper deals with a singular, nonlinear Sturm-Liouville problem of the form {A(x)u'(x)}'+ lambda u (x) = f (x, u(x), u'(x)) on (0,1) where A is positive on (0,1] but decays quadratically to zero as x approaches zero. This is the lowest level of degeneracy for which the problem exhibits behaviour radically different from the regular case. In this paper earlier results on the existence of bifurcation points are extended to yield global information about connected components of solutions.

UNIV SZEGED, BOLYAI INSTITUTE2020