We consider the Brascamp–Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of centred gaussian extremals. For arbitrary extremals we completely address the issue of existence, and partly address the issue of uniqueness. We also analyse th...

In this work we present some new results concerning the existence and uniqueness of solutions to an impulsive first-order, nonlinear ordinary differential equation with “non-periodic” boundary conditions. These boundary conditions include, as a special case, so-called “anti-periodic” boundary conditions. Our methods to prove the existence and uniqueness of solutions involve new differential ine...

Abstract: In this article, we discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations ( Dα − ρtDβ ) x(t) = f (t, x(t), Dγx(t)) , t ∈ (0, 1) with boundary conditions x(0) = x0, x(1) = x1 or satisfying the initial conditions x(0) = 0, x′(0) = 1 where D denotes Caputo fractional derivative, ρ is constant, 1 < α < 2 and 0 < β + γ ≤ 1. Schaurder...

We reprove in an extremely simple way the classical theorem that time periodic dissipative systems imply the existence of harmonic periodic solutions, in the case of uniqueness. We will also show that, in the lack of uniqueness, the existence of harmonics is implied by uniform dissipativity. The localization of starting points and multiplicity of periodic solutions will be established, under su...

The existence-uniqueness criteria of nonlinear fractional integro-differential equations variable order with multiterm boundary value conditions are considered in this work. By utilizing the concepts generalized intervals combined piecewise constant functions, we transform our problem into usual Caputo’s differential order. We develop necessary for assuring solution's existence and uniqueness b...

We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted Delaunay triangulations may be interpreted as images of hyperbolic polyhedra with one vertex on and the remaining vertices beyond the infinite boundary of hype...

We study constrained viscosity solutions with an unbounded growth for a class of first order Hamilton–Jacobi–Bellman equations arising in hybrid control systems. To deal with the boundary constraint and rapid growth of the solutions, we construct a particular set of test functions and under very mild conditions establish a comparison theorem which gives the estimate of distance between the subs...

Time-dependent density functional theory (TDDFT) for quantummany-body systems on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is v representable if the initial many-body state and the density satisfy certain well-defined conditions. In particular, we show that for a system evolving from its ground state any ...

In this paper we have considered the question of the existence of the solution of a pair of coupled ordinary differential equations depending on a parameters. By using a corollary of the SchauderTychonoff fixed point theorem, and some hard analysis needed to cover essentially the range of s near s=O we were able to show that all the conditions for the theorem could be fulfilled. Hence existence...

The solution to a sequential fractional differential equation with affine periodic boundary value conditions is investigated in this paper. existence theorem of established by means the Leray–Schauder fixed point and Krasnoselskii theorem. What more, uniqueness demonstrated via Banach contraction mapping principle. In order illustrate main results, two examples are listed.