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MULTIPLE SOLUTIONS FOR A HAMILTONIAN ELLIPTIC SYSTEM WITH SIGN-CHANGING PERTURBATION
《Acta Mathematica Scientia》2025年第2期602-614,共13页Peng CHEN Longjiang GU Yan WU 
supported by the NSFC(11301297);the Hubei Provincial Natural Science Foundation of China(2024AFB730);the Yichang City Natural Science Foundation(A-24-3-008);the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(NAA2024ORG003);Gu's research was supported by the Zhejiang Provincial Natural Science Foundation(LQ21A010014);the NFSC(12101577).
In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome...
关键词：variational method strongly indefinite elliptic system multiple solutions signchanging nonlinearity 
Positive Periodic Solutions to a Second-order Nonlinear Differential Equation with an Indefinite Singularity
《数学理论与应用》2025年第1期81-93,共13页YUAN Shujing LI Shaowen CHENG Zhibo 
supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025);the Natural Science Foundation of Henan Province(No.222300420449);the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...
关键词：Schauder fixed point theorem Krasnoselskii-Guo fixed point theorem Indefinite singular Sublinear and semilinear Positive periodic solution 
Robust Output Practical Stability of Time-Varying Nonlinear Control Systems via Indefinite Lyapunov Functions
《Journal of Systems Science & Complexity》2024年第6期2595-2613,共19页DAMAK Hanen ABOTHHER Amal HAMMAMI Mohamed Ali 
This paper focuses on studying the problem of robust output practical stability of timevarying nonlinear control systems. The main innovation lies in the fact that the proposed approach for stability analysis allows f...
关键词：Control theory global robust practical asymptotic output stability(GRPAOS) Lyapunov method time-varying control systems 
Indefinite metacavities coupled to a mirror:bound states in the continuum with anomalous resonance scaling
《Photonics Research》2024年第3期598-607,共10页QIANG ZHANG PEIXIANG LI ZHIYUAN GU SHAODING LIU ZEJUN DUAN 
National Natural Science Foundation of China(12004273,11574228,11874276,61905113);Key Research and Development Program of Shanxi Province(201903D121131)。
Indefinite metacavities(IMCs)made of hyperbolic metamaterials show great advantages in terms of extremely small mode volume due to large wave vectors endowed by the unique hyperbolic dispersion.However,quality(Q)facto...
关键词：HYPERBOLIC MIRROR definite 
Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs被引量：1
《Science China Mathematics》2024年第1期211-236,共26页Qi Lü Bowen Ma 
supported by National Natural Science Foundation of China (Grant Nos.12025105, 11971334 and 11931011);the Chang Jiang Scholars Program and the Science Development Project of Sichuan University (Grant Nos. 2020SCUNL101 and 2020SCUNL201)。
A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,...
关键词：linear-quadratic optimal control problem time-inconsistent cost functional generalized Riccati equation indefinite control weight cost closed-loop equilibrium strategy 
Accelerated Stochastic Peaceman–Rachford Method for Empirical Risk Minimization
《Journal of the Operations Research Society of China》2023年第4期783-807,共25页Jian-Chao Bai Feng-Miao Bian Xiao-Kai Chang Lin Du 
supported by the National Natural Science Foundation of China(Nos.12001430,11972292 and 12161053);the China Postdoctoral Science Foundation(No.2020M683545);the Guangdong Basic and Applied Basic Research Foundation(No.2023A1515012405).
This work is devoted to studying an accelerated stochastic Peaceman–Rachford splitting method(AS-PRSM)for solving a family of structural empirical risk minimization problems.The objective function to be optimized is ...
关键词：Empirical risk minimization Convex optimization Stochastic Peaceman-Rachford method Indefinite proximal term Complexity 
AN INDEFINITE-PROXIMAL-BASED STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD被引量：1
《Journal of Computational Mathematics》2023年第6期1017-1040,共24页Yan Gu Bo Jiang Deren Han 
supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20210267);supported by the National Natural Science Foundation of China (Grant No.11971239);the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.21KJA110002);supported by the National Natural Science Foundation of China (Grant Nos.12131004,11625105).
The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.However,its convergence was not guaranteed without extra requ...
关键词：Indefinite proximal Strictly contractive Peaceman-Rachford splitting method Convex minimization Convergence rate 
ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN(p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL
《Acta Mathematica Scientia》2022年第2期561-574,共14页Salvatore LEONARDI Nikolaos S.PAPAGEORGIOU 
supported by Piano della Ricerca di Ateneo 2020-2022-PIACERIProject MO.S.A.I.C;"Monitoraggio satellitare,modellazioni matematiche e soluzioni architettoniche e urbane per lo studio,la previsione e la mitigazione delle isole di calore urbano",Project EEEP&DLaD.S。
We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavio...
关键词：(p q)-Laplacian indefinite potential nonlinear regularity extremal constant sign solutions nodal solutions 
Erratum to “Solutions of Indefinite Equations”, [Advances in Pure Mathematics Vol. 10, No. 9, (2020) 540-544]
《Advances in Pure Mathematics》2022年第4期306-307,共2页Zengyong Liang 
The original online version of this article (Zengyong Liang (2020) Solutions of Indefinite Equations, Volume 10(9), 540-544, doi: https://doi.org/10.4236/apm.2020.109033) unfortunately contains some mistakes. The auth...
关键词：L-Algorithm 
非正则线性增广拉格朗日乘子法的收敛速率研究被引量：1
《高等学校计算数学学报》2022年第1期36-49,共14页马峰 倪明放 
Supported by the NSFC Grant 12171481;NSF of Shaanxi Province grant 2020JQ-485.
Recently,an indefinite linearized augmented Lagrangian method(IL-ALM)was proposed for the convex programming problems with linear constraints.The IL-ALM differs from the linearized augmented Lagrangian method in that ...
关键词：Convex programming augmented Lagrangian method proximal point algorithm convergence analysis indefinite regularization 
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