Bevan Thompson

Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces

In the present paper, we establish two fixed point theorems for upper semicontinuous multivalued mappings in hyperconvex metric spaces and apply these to study coincidence point problems and minimax problems.

Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal sampling

In this paper we have used simulations to make a conjecture about the coverage of a t-dimensional subspace of a d-dimensional parameter space of size n when performing k trials of Latin Hypercube sampling. This takes the form P(k,n,d,t) = 1 - e^(-k/n^(t-1)). We suggest that this coverage formula is independent of d and this allows us to make connections between building Populations of Models and Experimental Designs. We also show that Orthogonal sampling is superior to Latin Hypercube sampling in terms of allowing a more uniform coverage of the t-dimensional subspace at the sub-block size level. These ideas have particular relevance when attempting to perform uncertainty quantification and sensitivity analyses.

Systems of differential equations with implicit impulses and fully nonlinear boundary conditions

We show that systems of second-order ordinary differential equations, x″=f(t,x,x′), subject to compatible nonlinear boundary conditions and impulses, have a solution x such that (t,x(t)) lies in an admissible bounding subset of [0,1]×Rn when f satisfies a Hartman-Nagumo growth bound with respect to x′. We reformulate the problem as a system of nonlinear equations and apply Leray-Schauder degree theory. We compute the degree by homotopying to a new system of nonlinear equations based on the simpler system of ordinary differential equations, x″=M0L(x−v), subject to Picard boundary conditions and impulses and using the Leray index theorem. Our proof is simpler than earlier existence proofs involving nonlinear boundary conditions without impulses and requires weak assumptions on f.MSC:34A37, 34A34, 34B15.

Applications of maximum principles to dynamic equations on time scales

We apply the strong maximum principle to obtain a priori bounds and uniqueness of solutions for some initial value and boundary value problems as well as to establish oscillation results for second-order dynamic equations on time scales. Our comparison, uniqueness, and oscillation results are new and are extensions of results for ordinary differential equations to the times scale setting.

Stability of the equator map for the Hessian energy

In this paper we show that the equator map is a minimizer of the Hessian energy H(u) = integral Omega vertical bar Delta u vertical bar(2) dx in H-2(Omega;S-n) for n >= 10 and is unstable for 5 <= n <= 9.

Solvability of singular second order m -point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

First-Order Three-Point Boundary Value Problems at Resonance Part III

The main purpose of this paper is to investigate the existence of solutions of BVPs for a very general case in which both the system of ordinary differential equations and the boundary conditions are nonlinear. By employing the implicit function theorem, sufficient conditions for the existence of three-point boundary value problems are established.

Quasiequilibrium problem in H-spaces☆

In the present paper, we study the quasiequilibrium problem and generalized quasiequilibrium problem of generalized quasi-variational inequality in H-spaces by a new method. Some new equilibrium existence theorems are given. Our results are different from corresponding given results or contain some recent results as their special cases

A scalarization technique for computing the power and exponential moments of Gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A