Existence for Second Order Differential Inclusions on ℝ+ Governed by Monotone Operators

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Gheorghe Moroşanu
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Differential Inclusions ◽  
Real Hilbert Space ◽  
Monotone Operators ◽  
Second Order

AbstractConsider in a real Hilbert space H the differential equation (inclusion) (E): p(t)u″(t) + q(t)u′(t) ∈ Au(t) + f (t) for a.a. t ∈ ℝ

scholarly journals Boundary value problems for nonlinear systems with generalized second-order differences

2011 ◽  
Vol 27 (1) ◽  
pp. 95-104
Author(s):  
RODICA LUCA ◽  
Keyword(s):  
Boundary Condition ◽  
Hilbert Space ◽  
Nonlinear Systems ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Real Hilbert Space ◽  
Boundary Value ◽  
Monotone Operators ◽  
Second Order ◽  
Differential Systems

In a real Hilbert space, we investigate the existence and uniqueness of the solutions for two classes of infinite nonlinear systems with generalized second-order differences, one of them subject to a boundary condition. Some applications to nonlinear differential systems with monotone operators are also presented.

scholarly journals Positive functionals and oscillation criteria for second order differential systems

1979 ◽  
Vol 22 (3) ◽  
pp. 277-290 ◽  
Author(s):  
Garret J. Etgen ◽  
Roger T. Lewis
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Second Order ◽  
Linear Operators ◽  
The Self ◽  
Differential Systems ◽  
Bounded Linear ◽  
Positive Functionals ◽  
Image Position ◽  
Adjoint Operators

Let ℋ be a Hilbert space, let ℬ = (ℋ, ℋ) be the B*-algebra of bounded linear operators from ℋ to ℋ with the uniform operator topology, and let ℒ be the subset of ℬ consisting of the self-adjoint operators. This article is concerned with the second order self-adjoint differential equation

scholarly journals Differential game with switching controls on Hilbert space

1997 ◽  
Vol 39 (2) ◽  
pp. 230-256
Author(s):  
Siu Pang Yung
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Viscosity Solution ◽  
Real Hilbert Space ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Evolution System ◽  
Value Of The Game ◽  
Existence Of Value

AbstractWe study differential game problems in which the players can select different maximal monotone operators for the governing evolution system. Setting up our problem on a real Hilbert space, we show that the Elliott-Kalton upper and lower value of the game are viscosity solution of some Hamilton-Jacobi-Isaacs equations. Uniqueness is obtained by assuming condition analogous to the classical Isaacs condition, and thus the existence of value of the game follows.

scholarly journals A fixed point method to solve the nonlinear complementarity problem for a class of monotone operators

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4587-4590
Author(s):  
Dinu Teodorescu ◽  
Mohammad Khan
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Complementarity Problem ◽  
Real Hilbert Space ◽  
Nonlinear Complementarity Problem ◽  
Monotone Operators ◽  
Fixed Point Method ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Complementarity

In this paper, using the classic Banach fixed point theorem, we study the nonlinear complementarity problem for a class of monotone operators in real Hilbert space.

VII.—On the Spectrum of Ordinary Second Order Differential Operators.

1969 ◽  
Vol 68 (2) ◽  
pp. 95-119 ◽  
Author(s):  
Jyoti Chaudhuri ◽  
W. N. Everitt
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Analytic Function ◽  
Spectral Theory ◽  
Spectral Properties ◽  
Differential Operators ◽  
Second Order ◽  
Space Theory ◽  
Alternative Approach

SynopsisThis paper considers properties of the spectrum of differential operators derived from differential expressions of the second order. The object is to link the spectral properties of these differential operators with the analytic, function-theoretic properties of the solutions of the differential equation. This provides an alternative approach to the spectral theory of these differential operators but one which is consistent with the standard definitions used in Hilbert space theory. In this way the approach may be of interest to applied mathematicians and theoretical physicists.

scholarly journals New Tseng-Degree Gradient Method in Variational Inequality Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Zhuang Shan ◽  
Lijun Zhu ◽  
Long He ◽  
Danfeng Wu ◽  
Haicheng Wei
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
High Precision ◽  
Gradient Method ◽  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Monotone Operators ◽  
Inequality Problem ◽  
Convergence Performance

This paper focuses on the problem of variational inequalities with monotone operators in real Hilbert space. The Tseng algorithm constructed by Thong replaced a high-precision step. Thus, a new Tseng-like gradient method is constructed, and the convergence of the algorithm is proved, and the convergence performance is higher.

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