Abstract
This note discusses the asymptotic properties of the nonlinear differential equation x”+ a(t)f(x)x’+ b(t)g(x)=0. The behavior of non-oscillatory solutions are shown to be bounded and in L p [0,∞) under specified conditions. Furthermore, the derivative are shown to be in L 2 [0,∞) and the solutions as well as their derivatives shown to approach 0 as t→∞ implying stability. Finally, several examples illustrating these results are also given.
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