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Boundedness of solutions to fourth-order differential equation with oscillatory restoring and forcing terms. (English) Zbl 1141.34320

Summary: This paper concerns the fourth order differential equation \[ x''''+ax'''+f(x'')+g(x')+h(x)=p(t). \] Using the Cauchy formula for the particular solution of non-homogeneous linear differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
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