Nonlinear fourth-order elliptic equations with nonlocal boundary conditions |
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Authors: | CV Pao |
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Institution: | a Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA b Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China c Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, People's Republic of China |
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Abstract: | This paper is concerned with a class of fourth-order nonlinear elliptic equations with nonlocal boundary conditions, including a multi-point boundary condition in a bounded domain of Rn. Also considered is a second-order elliptic equation with nonlocal boundary condition, and the usual multi-point boundary problem in ordinary differential equations. The aim of the paper is to show the existence of maximal and minimal solutions, the uniqueness of a positive solution, and the method of construction for these solutions. Our approach to the above problems is by the method of upper and lower solutions and its associated monotone iterations. The monotone iterative schemes can be developed into computational algorithms for numerical solutions of the problem by either the finite difference method or the finite element method. |
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Keywords: | Fourth-order elliptic equation Nonlocal boundary condition Multi-point boundary condition Maximal and minimal solutions Method of upper and lower solutions Monotone iterations |
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