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Solvability of singular beam equations fixed at left and simply supported at right. (Chinese. English summary) Zbl 1174.34354
Summary: The existence of solutions for a class of singular beam equations fixed at left and simply supported at right is considered. By using Green’s function of the corresponding linear problem, the problem is transformed into an integral equation. By means of the Leray-Schauder nonlinear alternative, an existence theorem is established. The nonlinear term contains all orders of derivatives and satisfies an asymptotic growth condition.

MSC:
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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