Research On Nonlinear Type Conditional Input-Output Equation

Based on the classical theory of the matrix type input-output analysis, a type of nonlinear conditional Leontief model in continuous type and input-output equation were introduced, as well as the three corresponding questions on solvability, continuity and surjectivity. Then both the methods of differentiation coefficient and nonlinear analysis were applied in this research. As a result, some main theorems are obtained and the corresponding explanations are also given out.The paper comprises three parts.In the first part, the differentiation coefficient method was used to discuss and research on the nonlinear input-output equation with the corresponding results obtained, under the condition of the fluxional of the consume matrix.In the second part, with the consideration of the topology theory such as Leray-Schauder degrees and some simple in-equation, some boundary conditions, while the fixed point existing, were established, and used in the study of the nonlinear input-output equation, with some corresponding theory developed.In the third part, broadening the terms of the theorem got in the second part, the paper given several unself-motion fixed point theorem and investigated the nonlinear input-output equation in virtue of these theorem, and got breakthrough in this field finally.The boundary conditions of the fixed point researched in this paper are remarkably different from such known conditions as the Rothe, Krasnoselskii, Petryshen and Altman.