The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained resul...The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.展开更多
Presents the fixed point theorem for a class of β constrictive increasing operators without continuity and discusses the existence of solution of the integral equation with the discontinuous term in L 1(0,∞)...Presents the fixed point theorem for a class of β constrictive increasing operators without continuity and discusses the existence of solution of the integral equation with the discontinuous term in L 1(0,∞) by using this theorem.展开更多
In this paper. the fixed point theorem of increasing opera for with non-continuityis uilized to discuss foe exislence and uniqueness of positire solution for a class of nonlinear Volterra integral equations. An import...In this paper. the fixed point theorem of increasing opera for with non-continuityis uilized to discuss foe exislence and uniqueness of positire solution for a class of nonlinear Volterra integral equations. An important condition of continuity can bereplaced by weak condition.展开更多
We prove that a u0-concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0-concave operator under a wea...We prove that a u0-concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0-concave operator under a weaker condition.展开更多
文摘The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.
文摘Presents the fixed point theorem for a class of β constrictive increasing operators without continuity and discusses the existence of solution of the integral equation with the discontinuous term in L 1(0,∞) by using this theorem.
文摘In this paper. the fixed point theorem of increasing opera for with non-continuityis uilized to discuss foe exislence and uniqueness of positire solution for a class of nonlinear Volterra integral equations. An important condition of continuity can bereplaced by weak condition.
基金Supported by NSFC (10371068)NSFC(60174007)Science Foundation of Shanxi Province (20041003)
文摘We prove that a u0-concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0-concave operator under a weaker condition.
