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A local existence theorem for nonlinear elastic beam equations fixed at left and simply supported at right. (English) Zbl 1127.34308
Summary: A local existence theorem is established for a class of fourth-order two-point boundary value problems with all order derivatives by using Green function and integral equation. The theorem improves previous results. In mechanics, the class of problems describes the deflection of a elastic beam fixed at left and simply supported at right.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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