Stablility Of The Solution Set Of Some Nonlinear Problems

The stability of solution set for the nonlinear problems is an important researchsubject in nonlinear analysis theory. It is widely used in theoretical and pratical fieldssuch as mathematical programming, multi-objective programming theory, engineeringtechnology, mathematical economics and social economic systems. The stability ofsolution set includes various aspects such as upper-continuity, lower-continuity,essential component and connectedness of solution set. This thesis mainly studies thestability of solution set for some nonlinear problems, such as essential component ofthe solution set for symmetric vector quasi-equilibrium problems under the conditionof cone-convexity, the continuity of the weak global efficient solution mapping for theparametricset-valued vector equilibrium problems, and the connectedness andcompactness of solution set for the above problem, the connectedness of the globalefficient solution set and Henig efficient solution set for the parametic set-valuedvector equilibrium problems. The major work of the thesis is as follows:In the first chapter, we introduce the research background and history about somenonlinear problems. It also analyzes and summarizes the domestic and overseasscholars’ research achievements.In the second chapter, we discuss essential component of the solution set forsymmetric vector quasi-equilibrium problems under the condition of cone-convexity.we discussed the existence of the essential component of the solution set forsymmetric vector quasi-equilibrium problems under the suitable conditions ofcone-convexity and obtained an essential component existence theorem when theobjective functions and constraint mapping are perturbed.In the third chapter, we discuss the continuity of the weak global efficient solutionmapping for the parametric set-valued vector equilibrium problems. it first introducesthe concept of weak global efficient solution for the parametric set-valued vectorequilibrium problems, and obtains the scalarization results of the weak global efficientsolution for the parametric set-valued vector equilibrium problems. Basing on thescalarization results, it studies the continuity of the weak global efficient solutionmapping for the parametric set-valued vector equilibrium problems.In the fourth chapter, we discuss the connectedness and compactness of the weak global efficient solution set for the parametric set-valued vector equilibrium problems.After introducing the concept of weak global efficient solution, first, it discusses theconnectedness and compactness of the weak global efficient solution set for theparametricset-valued vector equilibrium problems in Hausdorff topological vectorspaces.In the fifth chapter, we discuss the connectedness of the global efficient solutionmapping and Henig efficient solution set for the parametic set-valued vectorequilibrium problems. We discuss the connectedness of the global efficient solutionset for the parametic set-valued vector equilibrium problems in Hausdorff topologicalvector spaces, and discuss the connectedness of the Henig efficient solution set in thenormed linear space.