Bounded solutions to x'' + q(t)b(x) = f(t): Allan Kroopnick

• Autores: Allan Kroopnick
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 41, Nº. 6, 2010, págs. 829-836
• Idioma: inglés
• DOI: 10.1080/00207391003777863
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• Resumen

  • This article discusses the conditions under which all solutions to x'' + q(t)b(x) = f(t) are bounded on [0, 8). These results are generalizations of the linear case. A short discussion of the properties of bounded oscillatory solutions for both the linear and nonlinear cases when f(t) =0, xb(x) > 0 and b'(x) > 0 for x ? 0 is also provided. Finally, we shall see that the previous arguments may be applied to the more general nonlinear differential equation x'' + c(t, x, x') + q(t)b(x) = f(t) with appropriate conditions on c(t, x, x').