Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4635825 | Applied Mathematics and Computation | 2007 | 5 Pages |
Abstract
Ulam’s problem for approximate homomorphisms and its application to certain types of differential equations was first investigated by Alsina and Ger. They proved in [C. Alsina, R. Ger, On some inequalities and stability results related to the exponential function, J. Inequal. Appl. 2 (1998) 373–380] that if a differentiable function f:I→Rf:I→R satisfies the differential inequality ∣y′(t) − y(t)∣ ⩽ ε, where I is an open subinterval of RR, then there exists a solution f0:I→Rf0:I→R of the equation y′(t) = y(t) such that ∣f(t) − f0(t)∣ ⩽ 3ε for any t ∈ I.In this paper, we investigate the Ulam’s problem concerning the Bernoulli’s differential equation of the form y(t)−αy′(t) + g(t)y(t)1−α + h(t) = 0.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Soon-Mo Jung, Themistocles M. Rassias,