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Monotonically iterative method of nonlinear cantilever beam equations. (English) Zbl 1154.74021
Summary: The positive solution is studied for a nonlinear fourth-order two-point boundary value problem. In mechanics, the problem is called cantilever beam equation. By making use of the monotonically iterative technique, a successively iterative sequence is constructed. By applying the successively approximate method, an existence theorem is proved.
MSC:
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
74H20Existence of solutions for dynamical problems in solid mechanics
74H15Numerical approximation of solutions for dynamical problems in solid mechanics