Abstract
This paper considers asymptotic behaviour of solutions of a nonlinear differential equation of second order where the coefficient of nonlinearity is a bounded function for arbitrarily large values of $x$ in $\mathbb{R}$. Here we obtained sufficient conditions for boundedness, convergence ofsolutions to zero as $x\rightarrow\infty$, and unboundedness of solutions.
Highlights
This paper considers asymptotic behaviour of solutions of a nonlinear differential equation of second order where the coefficient of nonlinearity is a bounded function for arbitrarily large values of x in R
Mathematical modelling of most natural, scientific and industrial phenomena is based on nonlinear differential equations which are not solvable
The study (Tong, 1982) showed that the nonlinear differential equation u + f (t, u)sgnu = 0 has solutions which are asymptotic to a + bt where a, b are constants and b 0
Summary
Mathematical modelling of most natural, scientific and industrial phenomena is based on nonlinear differential equations which are not solvable. Sufficient criteria of integral type were obtained by Mingareilli and Sadarangani in (2007) for non-oscillation and asymptotic behaviour of solutions of nonlinear differential equation u + F(x, y(x)) = g(x). They proved the existence of a positive asymptotically linear solution y(x) = ax + b + O(1), as x → ∞. While Lipovan in her study (2003) has obtained for a class of second order nonlinear differential equations, sufficient conditions that are presented to ensure that some, respectively all solutions are asymptotic to lines. We will consider in future the equation z h(
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