The discriminance methods and expression of generalized alternative optimum solutions of linear programming is given by proving that the equivalent of optimum extreme point and extreme point of optimum solution sets of linear programming and applying the theorem of convex polyhedron.

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Under the G-differentiable ,using the alternative theorem of generalized subconvexlike map and other some conclusions in locally-convex Hausdorff topological spaces, the optimality conditions of vector extremum problems with set constraint are established.

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Applying the theorem of alternative of subconvexlike map and other some conclusions, the optimality conditions represented by gradient for the vector extremum problems with generalized inequality constraint are obtained.

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In ordered linear topological space, the concept of (u,O_2,Y_ )- generalized subconvexlike map is defined, and some important properties of the concept are discussed, and the alternative theorem of the map is established.

在序線性拓撲空間中最近中文字幕免费视频在线，定義了(u，0_2www。射；Y_ )-廣義次似凸映射的概念91在线亚洲视屏，并討論了它的一些性質(zhì)，建立了此映射的擇一定理国产精品无码三级在线播放一区。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

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Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.

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By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskiis fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

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By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskii's fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

借助于錐上的非線性Leray-Schauder擇一型定理和郭-Krasnoselskii's不動點定理，我們建立了非線性奇異耦合分?jǐn)?shù)次微分方程組正解的存在性定理美国不卡av。

Since then,by applying the Leray-Schauder continuation theorem,nonlinear alternative of Leary-Schauder,coincidence degree theory,and Krasnoselskii's fixed point theorem,many researchers have studied more general nonl...

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By using the theorem of alternative,we obtain the necessary and sufficient conditions for strong efficient solutions to be the generalized saddle point in vector optimization problems with set-valued maps under the assumption of nearly cone-subconvexlikeness.

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