Abstract
In this note we present a boundedness theorem to the equation x″ + c(t, x, x′) + a(t)b(x) = e(t) where e(t) is a continuous absolutely integrable function over the nonnegative real line. We then extend the result to the equation x″ + c(t, x, x′) + a(t, x) = e(t). The first theorem provides the motivation for the second theorem. Also, an example illustrating the theory is then given.
Highlights
In this article we shall discuss using standard methods the boundedness properties of a second order nonlinear differential equation with integrable forcing term, i.e. the equation," + (, ’) + ()b() () (.l)Our purpose here is to simplify some of the previous proofs to this well-known equation as well as extending some of the previous results
In this note we present a boundedness theorem to the equation x"+ c(t,x,x’)+ a(t)b(x)= e(t)where e(t) is a continuous absolutely integrable function over the nonnegative real line
We extend the result to the equation x" + c(t, x, :r’) + a(t, x) e(t)
Summary
In this article we shall discuss using standard methods the boundedness properties of a second order nonlinear differential equation with integrable forcing term, i.e. the equation," + (,, ’) + ()b() () (.l)Our purpose here is to simplify some of the previous proofs to this well-known equation as well as extending some of the previous results. GENERAL BOUNDEDNESS THEOREMS TO SOME SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION In this note we present a boundedness theorem to the equation x"+ c(t,x,x’)+ a(t)b(x)= e(t)where e(t) is a continuous absolutely integrable function over the nonnegative real line. We extend the result to the equation x" + c(t, x, :r’) + a(t, x) e(t).
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