id: 05820479
dt: j
an: 2010f.00842
au: Kroopnick, Allan J.
ti: Bounded solutions to $x^{\prime \prime}+q(t)b(x)=f(t)$.
so: Int. J. Math. Educ. Sci. Technol. 41, No. 6, 829-836 (2010).
py: 2010
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: I75
ut: bounded; boundedness; absolutely integrable; oscillatory; continuously
differentiable; nonlinear differential equations
ci:
li: doi:10.1080/00207391003777863
ab: 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 $c(t,x,x^{\prime})$.
rv: