Positivity of the Green functions for higher order ordinary differential equations.
Potential Theory for Schrödinger operators on finite networks.
We aim here at analyzing the fundamental properties of positive semidefinite Schrödinger operators on networks. We show that such operators correspond to perturbations of the combinatorial Laplacian through 0-order terms that can be totally negative on a proper subset of the network. In addition, we prove that these discrete operators have analogous properties to the ones of elliptic second order operators on Riemannian manifolds, namely the monotonicity, the minimum principle, the variational treatment...
Precise asymptotic behavior of solutions to damped simple pendulum equations.
Pricing equity-linked debt using the Vasicek model.
Problème du chasseur au trosième ordre.
Problèmes aux limites pour des inclusions différentielles sans condition de croissance
Abstract. Applying the topological transversality method of Granas and the a priori bounds technique, we prove some existence theorems for diflerential inclusions of the form x" ∈ F(t, x, x'), x ∈ ℬ, where F is a Carathéodory multifunction with convex, compact values. No growth condition will be imposed on F.
Problems with nonlinear boundary value conditions
The existence and multiplicity results are shown for certain types of problems with nonlinear boundary value conditions.
Professor Miroslav Laitoch sexagenarian
Projection Methods and Singular Two Point Boundary Value Problems.
Projektive Newton-Verfahren und Anwendungen auf nichtlineare Randwertaufgaben.
Properties of non-hermitian quantum field theories
In this paper I discuss quantum systems whose Hamiltonians are non-Hermitian but whose energy levels are all real and positive. Such theories are required to be symmetric under , but not symmetric under and separately. Recently, quantum mechanical systems having such properties have been investigated in detail. In this paper I extend the results to quantum field theories. Among the systems that I discuss are and theories. These theories all have unexpected and remarkable properties. I discuss...
Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities
The paper investigates the structure and properties of the set S of all positive solutions to the singular Dirichlet boundary value problem u″(t) + au′(t)/t − au(t)/t 2 = f(t, u(t),u′(t)), u(0) = 0, u(T) = 0. Here a ∈ (−∞,−1) and f satisfies the local Carathéodory conditions on [0,T]×D, where D = [0,∞)×ℝ. It is shown that S c = {u ∈ S: u′(T) = −c} is nonempty and compact for each c ≥ 0 and S = ∪c≥0 S c. The uniqueness of the problem is discussed. Having a special case of the problem, we introduce...
Prüfer transformation for the -Laplacian.