A degree-theoretic approach to solution stability of parametric generalized equations governed by set-valued maps B. T. Kien ∗ , N.-C. Wong † and J.-C. Yao ‡ March 18, 2008 Abstract This paper is concerned with solvability and solution stability of parametric generalized equations governed by set-valued mappings. By a degree-theoretic approach for multifunctions, some new results on lower semicontinuity of the solution map to a parametric generalized equation are established. Keywords: Parametric generalized equation, solution stability, degree theory, Skryp- nik degree, (S ) + -multifunctions. 1 Introduction Let X , Y and M are norm spaces, F : X × M → 2 Y and T : X → 2 Y be given multifunctions. We are concerned with the parametric generalized equations of the form: 0 ∈ F (x, µ)+ T (x), (1) where µ ∈ M are parameters and x ∈ X is the primary variable. We are interested in undertaking a stability study of this equation as the parameter µ varies in a neighborhood of a given value µ 0 . Let us denote by S (µ) the solution set of (1) corresponding to paprameter µ ∈ M . Give a solution set S (µ 0 ); question that we shall investigate is the following: Does the equation (1) has solution when µ are * Department of Information and Technology, Hanoi National University of Civil Engineering, 55 Giai Phong Hanoi Vietnam; email: kienbt@nuce.edu.vn † Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 804. Email: wong@math.nsysu.edu.tw. ‡ Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan 804. Email: yaojc@math.nsysu.edu.tw. 1