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Related papers: On Non-Monotone Variational Inequalities

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By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.

Analysis of PDEs · Mathematics 2010-09-16 Simone Secchi

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

Functional Analysis · Mathematics 2013-11-05 Szilárd László

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…

Optimization and Control · Mathematics 2016-12-02 Giovanni P. Crespi , Andreas H. Hamel , Carola Schrage

In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…

Analysis of PDEs · Mathematics 2024-04-19 Xu Xian , Wang Taotao

This paper deals with quasi-variational inequality problems (QVIs) in a generic Banach space setting. We provide a theoretical framework for the analysis of such problems which is based on two key properties: the pseudomonotonicity (in the…

Optimization and Control · Mathematics 2018-12-04 Christian Kanzow , Daniel Steck

We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…

Exactly Solvable and Integrable Systems · Physics 2022-02-16 A. V. Domrin , M. A. Shumkin , B. I. Suleimanov

Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…

Classical Analysis and ODEs · Mathematics 2009-09-09 Nicusor Costea , Cezar Lupu

In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing…

Optimization and Control · Mathematics 2013-11-13 Cong D. Dang , Guanghui Lan

It is known that for convex sets, the KKM condition is equivalent to the finite intersection property. We use this equivalence to obtain a characterisation of monotone operators in terms of convex KKM maps and in terms of the existence of…

Optimization and Control · Mathematics 2015-03-24 Marc Lassonde

Given a conformally variational scalar Riemannian invariant $I$, we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with $I$ constant. We also…

Differential Geometry · Mathematics 2025-10-08 João Henrique Andrade , Jeffrey S. Case , Paolo Piccione , Juncheng Wei

A new approach to the solution of quasilinear nonelliptic first-order systems of inhomogeneous PDEs in many dimensions is presented. It is based on a version of the conditional symmetry and Riemann invariant methods. We discuss in detail…

Mathematical Physics · Physics 2015-05-19 A. Michel Grundland , Benoit Huard

We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain…

Optimization and Control · Mathematics 2016-12-02 Giovanni P. Crespi , MatteoRocca , Carola Schrage

Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms…

Optimization and Control · Mathematics 2026-04-16 Lingqing Shen , Fatma Kılınç-Karzan

In this paper, we present a novel stochastic method for solving variational inequalities (VI) in the context of Markovian noise. By leveraging Extragradient technique, we can productively solve VI optimization problems characterized by…

Optimization and Control · Mathematics 2026-05-18 Vladimir Solodkin , Michael Ermoshin , Roman Gavrilenko , Aleksandr Beznosikov

We study parabolic quasi-variational inequalities (QVIs) of obstacle type. Under appropriate assumptions on the obstacle mapping, we prove the existence of solutions of such QVIs by two methods: one by time discretisation through elliptic…

Optimization and Control · Mathematics 2020-05-27 Amal Alphonse , Michael Hintermüller , Carlos N. Rautenberg

Using a certain well-posed ODE problem introduced by Shilnikov in the sixties, G. Minervini proved in his PhD thesis [17], among other things, the Harvey-Lawson Diagonal Theorem but without the restrictive tameness condition for Morse…

Differential Geometry · Mathematics 2020-04-03 Daniel Cibotaru , Wanderley Pereira

In this paper, we study the existence of at least one positive solution for a nonlinear third-order two-point boundary value problem with integral condition. By employing the Krasnoselskii's fixed point theorem on cones, the existence…

Classical Analysis and ODEs · Mathematics 2018-12-11 Cheikh Guendouz , Faouzi Haddouchi , Slimane Benaicha

The Monotonocity Principle (MP), stating a monotonic relationship between a material property and a proper corresponding boundary operator, is attracting great interest in the field of inverse problems, because of its fundamental role in…

In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…

Analysis of PDEs · Mathematics 2023-03-14 Xusheng Du , Tianling Jin , Hui Yang

We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called \emph{weak Minty} solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of…

Optimization and Control · Mathematics 2023-06-21 Axel Böhm