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 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 Periodic Solutions of Second-Order Differential Inclusions Systems with -Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Liang Zhang ◽  
Peng Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Nonsmooth Critical Point Theory ◽  
Nonsmooth Critical Point ◽  
Existence Of Periodic Solutions

The existence of periodic solutions for nonautonomous second-order differential inclusion systems with -Laplacian is considered. We get some existence results of periodic solutions for system, a.e. , , by using nonsmooth critical point theory. Our results generalize and improve some theorems in the literature.

scholarly journals Positive periodic solutions for second order impulsive differential equations

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Jianhua Shen ◽  
Weibing Wang ◽  
Zhimin He
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Continuous Equation

AbstractThe existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using fixed point theorem in cone, new existence results of positive periodic solutions are obtained without assuming the existence of positive periodic solutions of the corresponding continuous equation.

scholarly journals Existence of Periodic Solutions for a Class of Asymptoticallyp-Linear Discrete Systems Involvingp-Laplacian

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Kai Chen ◽  
Qiongfen Zhang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Discrete System ◽  
Mountain Pass Theorem ◽  
Discrete Systems ◽  
Point Theory ◽  
Existence Results ◽  
Existence Of Periodic Solutions ◽  
Linear Discrete Systems

By applying Mountain Pass Theorem in critical point theory, two existence results are obtained for the following asymptoticallyp-linearp-Laplacian discrete systemΔ(|Δu(t−1)|p−2Δu(t−1))+∇[−K(t,u(t))+W(t,u(t))]=0. The results obtained generalize some known works.

Periodic solutions of non-autonomous second order systems with (q(t), p(t))-Laplacian

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
Daniel Paşca ◽  
Chun-Lei Tang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Action Principle ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Second Order Systems

AbstractUsing the least action principle in critical point theory we obtain some existence results of periodic solutions for (q(t), p(t))-Laplacian systems which generalize some existence results.

scholarly journals Positive Periodic Solutions for a Class of Strongly Coupled Differential Systems with Singular Nonlinearities

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ruipeng Chen ◽  
Guangchen Zhang ◽  
Jiayin Liu
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Positive Periodic Solutions ◽  
Differential Systems ◽  
Strongly Coupled ◽  
Singular Nonlinearities

This article studies the existence of positive periodic solutions for a class of strongly coupled differential systems. By applying the fixed point theory, several existence results are established. Our main findings generalize and complement those in the literature studies.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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