非线性算子方程的正算子解问题
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摘要
研究算子方程X~s+A~*X~(-q)A=Q(0算子方程有正算子解的一些必要条件和充分条件,并研究方程中各算子之间的关系。
In this paper,the conditions for the existence of positive operator solutions to the operator equation X~s+A~*X~(-q)A=Q(0
In this paper,the conditions for the existence of positive operator solutions to the operator equation X~s+A~*X~(-q)A=Q(0
引文
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[5]Y D M,P Z A.Positive solutions of nonlinear operator equations with sign-changing kernel and its applications[J].Applied Mathematics and Computation,2014,230(1):675-679.
[6]杨凯凡,张文鹏,窦艳妮.一类算子方程的正算子解[J].西北大学学报,2014,101(4):537-539.
[7]DENG C Y.On the solutions of operator equation[J].Journal of Mathematical Analysis and Applications,2013,398(2):664-670.
[8]YANG Y.The iterative method for solving nonlinear matrix equation Xs+A*X-tA=Q[J].Appl Math Comput,2007,188(1):46-53.
[9]SANG Yanbin.Multiple solutions for nonlinear operator equations under the condition of two pairs of paralleled lower and upper solutions[J].Mathematics with Applications,2012,63(8):1349-1353.
[10]CONWAY J B.A course in operator theory[M]Rhode Island:American Mathematical Society Providence,2000.
[11]BHATIA R.Matrix analysis,graduate texts in mathematics[M]New York:Springer-Verlag,1997.
[2]GREEN W L,KAMEN E.Stabilization of linear systems over acommutative normed algebra with applications to spatially distributed parameter dependent systems[J].SIAM J Control Optim,1985(23):1-18.
[3]BUCY R S.A priori bound for the Riccati equation,in:proceedings of the sixth Berkeley symposium on mathematical statistics and probability,probability theory[M]Berkeley:University of California Press,1972:645-656.
[4]YANG Y,DUAN F,ZHAO X.On solutions for the matrix equation Xs+A*X-tA=Q[J].Proc of the Seventh Int Conf on Matrix Theory and Its Applications in China,2006,50(6):21-24.
[5]Y D M,P Z A.Positive solutions of nonlinear operator equations with sign-changing kernel and its applications[J].Applied Mathematics and Computation,2014,230(1):675-679.
[6]杨凯凡,张文鹏,窦艳妮.一类算子方程的正算子解[J].西北大学学报,2014,101(4):537-539.
[7]DENG C Y.On the solutions of operator equation[J].Journal of Mathematical Analysis and Applications,2013,398(2):664-670.
[8]YANG Y.The iterative method for solving nonlinear matrix equation Xs+A*X-tA=Q[J].Appl Math Comput,2007,188(1):46-53.
[9]SANG Yanbin.Multiple solutions for nonlinear operator equations under the condition of two pairs of paralleled lower and upper solutions[J].Mathematics with Applications,2012,63(8):1349-1353.
[10]CONWAY J B.A course in operator theory[M]Rhode Island:American Mathematical Society Providence,2000.
[11]BHATIA R.Matrix analysis,graduate texts in mathematics[M]New York:Springer-Verlag,1997.