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. Here we obtained sufficient conditions for boundedness, convergence of solutions to zero as x → ∞, and unboundedness of solutions.
This paper considers the stability of differential equation of Mackey-Glass type in the sense of Hyers and Ulam with initial condition. It also considers the Hyers-Ulam stability of Lasota equation with initial condition. Some illustrative examples are given.
In this paper we established the Hyers-Ulam stability of a nonlinear differential equation of second order with initial condition. We also proved the Hyers -Ulam stability of a linear differential equation of second order with initial condition.
In this paper we have established the stability of a generalized nonlinear second-order differential equation in the sense of Hyers and Ulam. We also have proved the Hyers-Ulam stability of Emden-Fowler type equation with initial conditions.
In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in with initial condition, in the sense of Hyers-Ulam-Rassias. We have also used Laplace transform to establish the modified Hyers-Ulam-Rassias stability of initial-boundary value problem for heat equation on a finite rod. Some illustrative examples are given. n
In this paper, we introduce a new function ( ) [ ] ,, with x 2, which we call the greatest prime function. In addition, we give an extension of the function to R , and then use this definition to prove some inequalities and properties of this function. Some illustrative examples are given.
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