scholarly journals Nonlinear systems with a partial Nash type equilibrium

2021 ◽  
Vol 66 (2) ◽  
pp. 397-408
Author(s):  
Andrei Stan
Keyword(s):  
Variational Principle ◽  
Nonlinear Systems ◽  
Critical Point ◽  
Iterative Scheme ◽  
Existence Results ◽  
Ekeland's Variational Principle ◽  
Operator Equations ◽  
Energy Functionals ◽  
Variational Structure ◽  
Variational Form

"In this paper xed point arguments and a critical point technique are combined leading to hybrid existence results for a system of three operator equations where only two of the equations have a variational structure. The components of the solution which are associated to the equations having a variational form represent a Nash-type equilibrium of the corresponding energy functionals. The result is achieved by an iterative scheme based on Ekeland's variational principle."

scholarly journals Fixed point–critical point hybrid theorems and application to systems with partial variational structure

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Irene Benedetti ◽  
Tiziana Cardinali ◽  
Radu Precup
Keyword(s):  
Fixed Point ◽  
Critical Point ◽  
Periodic Solutions ◽  
Existence Results ◽  
Operator Equations ◽  
Variational System ◽  
Variational Structure

AbstractIn this paper, fixed point arguments and a critical point technique are combined leading to hybrid existence results for a system of two operator equations where only one of the equations has a variational structure. An application to periodic solutions of a semi-variational system is given to illustrate the theory.

scholarly journals Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity inR3

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ling Ding ◽  
Lin Li ◽  
Jin-Ling Zhang
Keyword(s):  
Variational Principle ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Kirchhoff Equation ◽  
Mountain Pass ◽  
Asymptotically Linear ◽  
Ekeland's Variational Principle

We study the following nonhomogeneous Kirchhoff equation:-(a+b∫R3‍|∇u|2dx)Δu+u=k(x)f(u)+h(x),  x∈R3,  u∈H1(R3),  u>0,  x∈R3, wherefis asymptotically linear with respect totat infinity. Under appropriate assumptions onk,f, andh, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.

scholarly journals New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 11
Author(s):  
Junjian Zhao ◽  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Critical Point ◽  
Point Theorem ◽  
Maximal Element ◽  
Existence Theorems ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Fuzzy Fixed Point ◽  
Element Theorem

In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland’s variational principle and common (fuzzy) fixed point theorem for essential distances.

The Existence of Solutions for Nonlinear Operator Equations

2008 ◽  
Vol 15 (1) ◽  
pp. 45-52
Author(s):  
Marek Galewski
Keyword(s):  
Nonlinear Operator ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Nonlinear Operator Equation ◽  
Global Minima ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Dual Variational Method ◽  
Dual Action ◽  
Primal And Dual

Abstract We provide the existence results for a nonlinear operator equation Λ*Φ′ (Λ𝑥) = 𝐹′(𝑥), in case 𝐹 – Φ is not necessarily convex. We introduce the dual variational method which is based on finding global minima of primal and dual action functionals on certain nonlinear subsets of their domains and on investigating relations between the minima obtained. The solution is a limit of a minimizng sequence whose existence and convergence are proved. The application for the non-convex Dirichlet problem with P.D.E. is given.

scholarly journals Remarks on Ume’s u−distance and Ekeland’s variational principle

2012 ◽  
Vol 28 (2) ◽  
pp. 257-264
Author(s):  
GEORGIANA GOGA ◽  
Keyword(s):  
Variational Principle ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Flower Petal ◽  
Flower Petal Theorem

The purpose of this paper is to present some remarks on Ume’s new concept of distance called u-distance, which generalizes w-distance and Suzuki’s t-distance. As an application of the u-distance version of Ekeland’s variational principle, we establish a generalized flower petal theorem.

Sign in / Sign up

Export Citation Format

Share Document