The Experts below are selected from a list of 180 Experts worldwide ranked by ideXlab platform
Lin-zhang Lu - One of the best experts on this subject based on the ideXlab platform.
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Effects of a parameter on a nonsymmetric algebraic Riccati equation
Applied Mathematics and Computation, 2005Co-Authors: Lin-zhang Lu, Michael K. NgAbstract:In this paper, we are interested in a nonsymmetric algebraic Riccati equation arising in transport theory. The effects of a parameter @a on the Minimal Positive Solution X*(@a) of this equation are studied. We show that X*(@a) decreases in @a only when @a is close to one and X*(@a) cannot attain its maximum for @[email protected]?[0,1). A matrix lower bound and a matrix upper bound for X*(@a) are also given.
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Solution Form and Simple Iteration of a Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory
SIAM Journal on Matrix Analysis and Applications, 2005Co-Authors: Lin-zhang LuAbstract:We are interested in computing the Minimal Positive Solution of a nonsymmetric algebraic Riccati equation arising in transport theory. We show that this computation can be done via computing only the Minimal Positive Solution of a vector equation, which is derived from the special form of Solutions of the Riccati equation. A simple iterative method is presented for solving the vector equation. The simple iteration is much more efficient than the Gauss--Jacobi method presented by Juang in [Linear Algebra Appl., 230 (1995), pp. 89--100] for the Riccati equation. The symmetric case and bounds of the Minimal Positive Solution are also considered. Numerical experiments are given.
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Newton iterations for a non-symmetric algebraic Riccati equation
Numerical Linear Algebra With Applications, 2005Co-Authors: Lin-zhang LuAbstract:The computation of the Minimal Positive Solution of a non-symmetric algebraic Riccati equation arising in transport theory is considered. It was shown in (SIAM J Matrix Anal Appl, submitted) that this can be done via only computing the Minimal Positive Solution of a vector equation, which is derived from special form of the Solutions of the Riccati equation and by exploitation of the special structure of the coefficient matrices of the Riccati equation. In this paper, the Newton method is developed for the vector equation. The Newton method is more simple and efficient than the corresponding Newton method directly for original Riccati equation and can preserve the form that any Solution of the Riccati equation must satisfy. Combination of the simple iteration and the Newton iteration is also considered. Numerical examples are given. Copyright © 2004 John Wiley & Sons, Ltd.
Nikolaos S. Papageorgiou - One of the best experts on this subject based on the ideXlab platform.
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Singular Dirichlet $(p,q)$-equations
arXiv: Analysis of PDEs, 2020Co-Authors: Nikolaos S. Papageorgiou, Patrick WinkertAbstract:We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian and with a reaction having the combined effects of a singular term and of a parametric $(p-1)$-superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of Positive Solutions as the parameter $\lambda>0$ varies. Moreover, we prove the existence of a Minimal Positive Solution $u^*_\lambda$ and study the monotonicity and continuity properties of the map $\lambda \to u^*_\lambda$.
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Parameter dependence for the Positive Solutions of nonlinear, nonhomogeneous Robin problems
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales. Serie A. Matemáticas, 2020Co-Authors: Nikolaos S. Papageorgiou, Calogero Vetro, Francesca VetroAbstract:We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is $$(p-1)$$ ( p - 1 ) -superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for Positive Solutions and prove a bifurcation-type result for the set of Positive Solutions as the parameter $$\lambda >0$$ λ > 0 varies. Also we prove the existence of a Minimal Positive Solution $$u_\lambda ^*$$ u λ ∗ and determine the monotonicity and continuity properties of the map $$\lambda \rightarrow u_\lambda ^*$$ λ → u λ ∗ .
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Perturbations of nonlinear eigenvalue problems
Communications on Pure and Applied Analysis, 2018Co-Authors: Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan RepovšAbstract:We consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both sublinear and superlinear perturbations and we determine how the set of Positive Solutions changes as the real parameter \begin{document}$λ$\end{document} varies. We also show that there exists a Minimal Positive Solution \begin{document}$\overline{u}_λ$\end{document} and determine the monotonicity and continuity properties of the map \begin{document}$λ\mapsto\overline{u}_λ$\end{document} . Special attention is given to the particular case of the \begin{document}$p$\end{document} -Laplacian.
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Positive Solutions for parametric semilinear Robin problems with indefinite and unbounded potential
Mathematica Scandinavica, 2017Co-Authors: Nikolaos S. Papageorgiou, Vicenţiu D. RădulescuAbstract:We consider a parametric Robin problem driven by the Laplace operator plus an indefinite and unbounded potential. The reaction term is a Caratheodory function which exhibits superlinear growth near $+\infty $ without satisfying the Ambrosetti-Rabinowitz condition. We are looking for Positive Solutions and prove a bifurcation-type theorem describing the dependence of the set of Positive Solutions on the parameter. We also establish the existence of the Minimal Positive Solution $u^*_{\lambda }$ and investigate the monotonicity and continuity properties of the map $\lambda \mapsto u^*_{\lambda }$.
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Robin problems with indefinite linear part and competition phenomena
Communications on Pure and Applied Analysis, 2017Co-Authors: Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan RepovšAbstract:We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a superlinear (convex) term. The superlinearity is not expressed via the Ambrosetti-Rabinowitz condition. Instead, a more general hypothesis is used. We prove a bifurcation-type theorem describing the set of Positive Solutions as the parameter $\lambda > 0$ varies. We also show the existence of a Minimal Positive Solution $\tilde{u}_\lambda$ and determine the monotonicity and continuity properties of the map $\lambda \mapsto \tilde{u}_\lambda$.
Changfeng Ma - One of the best experts on this subject based on the ideXlab platform.
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Some accelerated iterative algorithms for solving nonsymmetric algebraic Riccati equations arising in transport theory
International Journal of Computer Mathematics, 2019Co-Authors: Baohua Huang, Changfeng MaAbstract:AbstractIn this paper, some accelerated iterative algorithms are developed to find the Minimal Positive Solution of the nonsymmetric algebraic Riccati equation arising in transport theory. The conv...
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Some predictor–corrector‐type iterative schemes for solving nonsymmetric algebraic Riccati equations arising in transport theory
Numerical Linear Algebra With Applications, 2014Co-Authors: Na Huang, Changfeng MaAbstract:SUMMARY It is as well known that nonsymmetric algebraic Riccati equations arising in transport theory can be translated to vector equations. In this paper, we propose six predictor–corrector-type iterative schemes to solve the vector equations. And we give the convergence of these schemes. Unlike the previous work, we prove that all of them converge to the Minimal Positive Solution of the vector equations by the initial vector (e,e), where e = (1,1, ⋯ ,1)T. Moreover, we prove that all the sequences generated by the iterative schemes are strictly and monotonically increasing and bounded above. In addition, some numerical results are also reported in the paper, which confirm the good theoretical properties of our approach. Copyright © 2014 John Wiley & Sons, Ltd.
Ori Gurel-gurevich - One of the best experts on this subject based on the ideXlab platform.
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A Note on Costs Minimization with Stochastic Target Constraints.
arXiv: Probability, 2019Co-Authors: Yan Dolinsky, Benjamin Gottesman, Ori Gurel-gurevichAbstract:We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the Minimal Positive Solution of a second order semi--linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.
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Costs Minimization with Stochastic Target Constraints
arXiv: Probability, 2019Co-Authors: Yan Dolinsky, Benjamin Gotteman, Ori Gurel-gurevichAbstract:We study the minimization of the expected costs under stochastic constraint at the terminal time. Our first main result says that for a power type of costs, the value function is the Minimal Positive Solution of a second order semi--linear ordinary differential equation (ODE). Our second main result establishes the optimal control. In addition we show that the case of exponential costs leads to a trivial optimal control. All our proofs are based on the martingale approach.
Nicolae Tarfulea - One of the best experts on this subject based on the ideXlab platform.
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existence of the Minimal Positive Solution of some nonlinear elliptic systems when the nonlinearity is the sum of a sublinear and a superlinear term
Applied Mathematics and Mechanics-english Edition, 2000Co-Authors: Nicolae TarfuleaAbstract:It is shown that there exists Λ>0 such that, for every λe(0, Λ), the semilinear elliptic system: Δu = λu | u |q-1 + u | u |p-1 - υ, in ω, u=v=0 on ∂ ω, where ω eR N(N≥2) is a bounded domain with smooth boundary and 0
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Existence of the Minimal Positive Solution of some nonlinear elliptic systems when the nonlinearity is the sum of a sublinear and a superlinear term
Applied Mathematics and Mechanics, 2000Co-Authors: Nicolae TarfuleaAbstract:It is shown that there exists Λ>0 such that, for every λε(0, Λ), the semilinear elliptic system: Δu = λu | u |^q-1 + u | u |^p-1 - υ, in ω, u=v=0 on ∂ ω, where ω ε R ^N(N≥2) is a bounded domain with smooth boundary and 0