We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.

No abstract

No abstract

In this paper, we are concerned with the oscillations in forced second order nonlinear differential equations with nonlinear damping terms. By using clasical variational principle and averaging technique, new oscillation criteria are established, which revise, improve and extend some recent results. Furthermore our study answers the comment [16]. Examples are also given to illustrate the results.

Abstract:In this paper, we compute explicitly the oscillation constant for certain half-linear second-order differential equations having different periodic coefficients. Our result covers known result concerning half-linear Euler type differential equations with˛ periodic positive coefficients. Additionally, our result is new and original in case that the least common multiple of these periods is not defined. We give an example and corollaries which illustrate cases that are solved with our result.

Highlights • The paper focused on the stability of Hyers-Ulam, Hyers-Ulam-Rassias and Hyers-Ulam-Rassias-Gavruta. • This is the generalization of many previous studies. • The equation includes linear, Bernoulli, Riccati and Abel equations. • It is also the first work related to the stability of Abel equations in the literature.

No abstract

In this paper, we deal with the Hyers-Ulam-Rassias (HUR) and Hyers-Ulam (HU) stability of Hadamard type fractional integral equations on compact intervals. The stability conditions are developed using a new generalized metric (GM) definition and the fixed point technique by motivating Wang and Lin Ulam's type stability of Hadamard type fractional integral equations. Filomat 2014; 28(7): 1323-1331. Moreover, our approach is efficient and ease in use than to the previously studied approaches. Finally, we give two examples to explain our main results.