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Existence Theorems of Nonlinear Elastic Beam Equations with Fixed End and Movable End


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Existence Theorems of Nonlinear Elastic Beam Equations with Fixed End and Movable End
YAO Qing-liu
Department of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210003,China
nonlinear differential equation boundary value problem solution and posit ive solution existence fixed point theorem
The existence of solution and positive solut ion is considered for a class of nonlinear fourth-order elast ic beam equations. In mechanics, the class of equations describes deformation of the elast ic beam in which an end is f ixed and the other end is clamped by sliding clamps. By applying the decomposition technique of equations and constructing suitable Banach space, the class of differential equations is transformed to the fixed point equations in Banach spaces. By using Leray-Schauder fixed point theorem, four existence theorems are established for the class of equations. The main results show that the class of equations has at least one solution or posit ive solution if the / height0 of nonlinear term is appropriate on a bounded set .


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Last Update: 2013-05-29