We study in this paper a class of preference relations on two distinct vector spaces representing two production choice spaces by introducing a comparison theorem for stochastic differential equations driven by a semimartingale. Some sufficient conditions on production choices which are budget-constrained by commodity prices are proposed. Key–Words:stochastic differential equations, comparison ...

In this article we study entire solutions for a non-local delayed lattice differential equation with monostable nonlinearity. First, based on a concavity assumption of the birth function, we establish a comparison theorem. Then, applying the comparison theorem, we show the existence and some qualitative features of entire solutions by mixing a finite number of traveling wave fronts with a spati...

We propose a variant of Cauchy’s Lemma, proving that when a convex chain on one sphere is redrawn (with the same lengths and angles) on a larger sphere, the distance between its endpoints increases. The main focus of this work is a comparison of three alternate proofs, to show the links between Toponogov’s Comparison Theorem, Legendre’s Theorem and Cauchy’s Arm Lemma.

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

‎In this paper‎, ‎we develop the theory of hybrid differential‎ ‎equations on time scales‎. ‎An existence theorem for hybrid‎ ‎differential equations on time scales is given under Lipschitz ‎conditions‎. ‎Some fundamental fractional differential inequalities‎ ‎are also established which are utilized to prove the existence of‎ ‎extremal solutions‎. ‎Necessary tools are considered and the‎ ‎compa...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

A theorem of Blackwell about comparison between information structures in classical statistics is given an analogue in the quantum probabilistic setup. The theorem provides an operational interpretation for tracepreserving completely positive maps, which are the natural quantum analogue of classical stochastic maps. The proof of the theorem relies on the separation theorem for convex sets and o...