Bewley 14, Theorem l] proved an infinite dimensional equilibrium existence theorem which is a significant extension of the classical finite dimensional theorem of Arrow and Debreu [ 11. The assumptions on technology and preferences are natural and applicable in a wide variety of cases. The proof is based on a limit argument that makes direct use of the existence of equilibrium in the finite dim...

This paper is concerned with the Cauchy problem of nonlinear fourth-order Schrödinger equation on $ \mathbb{R}^{n} $, nonlinearity Hartree-type (|\cdot|^{-\gamma}\ast|u|^{2})u $. The existence a global solution to established when initial data belongs L^{p}(p<2) Moreover, given by using data-decomposition argument, two kinds generalized Strichartz estimates, and interpolation theorem.

Existence and uniqueness theorem for state-dependent delay-differential equations of neutral type is given. This theorem generalizes previous results by Grimm and the author.

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

Abstract: This paper deals with existence of solutions to three-point BVPs in perturbed systems of first-order ordinary differential equations at resonance. An existence theorem is established by using the Theorem of Borsuk and some examples are given to illustrate it. A result for computing the local degree of polynomials whose terms of highest order have no common real linear factors is also ...

In this paper, we design and analyze a Hybrid-High Order (HHO) approximation for class of quasilinear elliptic problems nonmonotone type. The proposed method has several advantages, instance, it supports arbitrary order general polytopal meshes. key ingredients involve local reconstruction high-order stabilization terms. Existence uniqueness the discrete solution are shown by Brouwer's fixed po...

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...