Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems

Monotone Iterative Method of Positive Solution to Boundary Value Problem of Nonlinear Differential Equation

Author SunJing
Tutor YaoQingLiu
School Nanjing University of Finance and Economics
Course Applied Mathematics
Keywords monotone iterative schemes nonlinear ordinary differential equation singlar boundary value problem positive solution
CLC O175.8
Type Master's thesis
Year 2011
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In this paper, several types of nonlinear boundary value problems are given Iteration of Positive Solutions of the format, the text of linear equations using the Green function corresponding to these equations into the integral equation, according to the corresponding integral operator constructed monotone iterative scheme, by controlling the nonlinear term in a bounded set of "high" to prove the convergence of monotone iterative schemes, the main tool is the monotone iterative method and the completely continuous operator theory of cone compression This iteration scheme starting from a constant function, so it is feasible and effective. This study these types of nonlinear boundary value problems with different features, such as the first study is a class of nonlinear singular elastic beam equations with monotone iterative scheme, followed by the introduction of the concept of symmetric positive solutions under study Boundary Value Problems for a Class of Symmetric Positive Solutions of Nonlinear Iterative format, and then studied for a Class of Second Order Boundary Value Iteration of Positive Solutions of the format, and then study the nonlinear second order Neumann boundary value Monotone Positive Solution format. Finally, using Schauder fixed point theorem, a class of second derivative of the fourth order boundary value problem solution and positive solution of the problem.

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