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\iteman{ZMATH 2010f.00842}
\itemau{Kroopnick, Allan J.}
\itemti{Bounded solutions to $x^{\prime \prime}+q(t)b(x)=f(t)$.}
\itemso{Int. J. Math. Educ. Sci. Technol. 41, No. 6, 829-836 (2010).}
\itemab
Summary: This article discusses the conditions under which all solutions to $x^{\prime \prime}+q(t)b(x)=f(t)$ are bounded on $[0,\infty)$. 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 $b^{\prime}(x)>0$ for $x\ne 0$ is also provided. Finally, we shall see that the previous arguments may be applied to the more general nonlinear differential equation $x^{\prime \prime}+c(t,x,x^{\prime})+q(t)b(x)=f(t)$ with appropriate conditions on $c(t,x,x^{\prime})$.
\itemrv{~}
\itemcc{I75}
\itemut{bounded; boundedness; absolutely integrable; oscillatory; continuously differentiable; nonlinear differential equations}
\itemli{doi:10.1080/00207391003777863}
\end