Related papers: An Existence Result for the Generalized Vector Equ…
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave…
In this paper, we study the existence of solutions in non-monotone variational inequalities (VIs) through the normal mapping properties. In particular, we show that when the normal mapping $F_K^{\rm nor}(\cdot)$ is norm coercive over a set…
In this paper we consider rough differential equations on a smooth manifold $\left( M\right) .$ The main result of this paper gives sufficient conditions on the driving vector-fields so that the rough ODE's have global (in time) solutions.…
We study the steady state solutions of a generalized logistic type equation on a complete Riemannian manifold. We provide sufficient conditions for existence, respectively non-existence of positive solutions, which depend on the relative…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
We extend the important generalizations by Yannelis [25] and Cornet et al [7] of the classical result of Gale, Nikaido, Kuhn and Debreu (the "GNKD theorem") regarding existence of market equilibrium, by broadening the applicability of their…
In this paper, we address the optimization problem of minimizing $Q(df_x)$ over a Hadamard manifold ${\cal M}$, where $f$ is a convex function on ${\cal M}$, $df_x$ is the differential of $f$ at $x \in {\cal M}$, and $Q$ is a function on…
This paper is devoted to study the qualitative properties of hybrid measure differential equations (HMDEs, for short). We establish several results on the existence of global solutions, including the existence of regulated, continuous,…
In this paper some Hadamard_type inequalities for product of convex functions of 2-variables on the co-ordinates are given.
In this paper, we propose a resolvent of an equilibrium problem in a geodesic space with negative curvature having the convex hull finite property. We prove its well-definedness as a single-valued mapping whose domain is whole space, and…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
In two and three space dimensions, and under suitable assumptions on the initial data, we show global existence for a damped wave equation which approaches, in some sense, the Navier-Stokes problem. The proofs are based on a refined energy…
The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient…
We present a Virtual Element Method (VEM) for the solution of Dirichlet problems for the quasilinear equation $-\text{div} (k(u)\text{grad} u)=f$ with essential boundary conditions. Within the VEM the nonlinear coefficient is evaluated with…
We establish differentiability properties of the value function of problems of Static Optimization in an abstract infinite dimensional setting and we apply that to problems of Calculus of Variations. We lighten the assumptions of existing…
Any individual's preference represents his choice in the set of available options. It is said to be complete if the person can compare any pair of available options. We aim to initiate the notion of projected solutions for the generalized…
We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization…
The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary…
The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…