Half-linear Functional Differential Equations Research Articles

New Criteria on Oscillatory Behavior of Third Order Half-Linear Functional Differential Equations

This paper deals with some new criteria for the oscillation of third order half-linear differential equations. The purpose of the present paper is the linearization of equation 1.1 in the sense that we would deduce oscillation of studied equation from that of the linear form and to provide new oscillation criteria via comparison with first order equations whose oscillatory behavior are known. The obtained results are new, improve and correlate many of the known oscillation criteria appeared in the literature for equation 1.1. The results are illustrated by some examples.

Criteria for Oscillation of Half-Linear Functional Differential Equations of Second-Order

The present article aims to establish more effective criteria for testing the oscillation of a class of functional differential equations with delay arguments. In the non-canonical case, we deduce some improved monotonic and asymptotic properties of the class of decreasing positive solutions of the studied equation. Depending on both the new properties and the linear representation of the studied equation, we obtain new oscillation criteria. Moreover, we test the effectiveness of the new criteria by applying them to some special cases of the studied equation.

Oscillation of half-linear differential equations with mixed type of argument

This paper is devoted to the study of the oscillatory behavior of half-linear functional differential equations with deviating argument of the form ( E ) ( r ( t ) ( y ′ ( t ) ) α ) ′ = p ( t ) y α ( τ ( t ) ) . . We introduce new technique based on monotonic properties of nonoscillatory solutions to offer new oscillatory criteria for ( E ) . We will show that presented results essentially improve existing ones even for linear differential equations.

On the oscillation of second-order half-linear functional differential equations with mixed neutral term

In this article, the authors establish new sufficient conditions for the oscillation of solutions to a class of second-order half-linear functional differential equations with mixed neutral term. The results obtained improve and complement some known results in the relevant literature. Examples illustrating the results are included.

Oscillation Criteria for Even-Order Half-Linear Functional Differential Equations with Damping

Oscillation Criteria for Even-Order Half-Linear Functional Differential Equations with Damping

Oscillation Criteria for Even-Order Half-Linear Functional Differential Equations with Damping

In this paper, a class of even-order half-linear functional differential equations with damping is studied. By using the generalized Riccati transformation and the integral averaging technique, six new oscillation criterias are obtained for all solutions of the equations. The results obtained generalize and improve some known results. Full Text: PDF DOI: http://dx.doi.org/10.11591/telkomnika.v12i6.5849

Oscillation criteria for half-linear function differential equations with damping

In this paper, a class of half-linear functional differential equations with damping are studied. By using the generalized Riccati transformation and integral average skills, new oscillation criteria are obtained which generalize and improve some known results.

Properties of higher-order half-linear functional differential equations with noncanonical operators

Some new results are presented for the oscillatory and asymptotic behavior of higher-order half-linear differential equations with a noncanonical operator. We study the delayed and advanced equations subject to various conditions.MSC:34C10, 34K11.

Oscillation criteria for even-order half-linear functional differential equations with damping

In this paper, a class of even-order half-linear functional differential equations with damping are studied. By using the generalized Riccati transformation and the integral averaging technique, new oscillation criteria are obtained for all solutions of the equations, which generalize and improve some known results.

Oscillation of even-order half-linear functional differential equations with damping

In this paper, a class of even-order half-linear functional differential equations with damping are studied. By using the generalized Riccati transformation and the integral averaging technique, the new oscillation criteria, which generalize and improve some known results, are obtained for all solutions of the equations.

Existence of regularly varying solutions with nonzero indices of half-linear differential equations with retarded arguments

Sharp conditions are established for the existence of a pair of regularly varying solutions with nonzero indices of half-linear functional differential equations of the type ( | x ′ ( t ) | α sgn x ′ ( t ) ) ′ = q ( t ) | x ( g ( t ) ) | α sgn x ( g ( t ) ) , α > 0 , q ( t ) > 0 , g ( t ) < t .

Regularly varying solutions of half-linear functional differential equations with retarded arguments

We consider half-linear retarded functional differential equations of the form $$ (|x'(t)|^\alpha \operatorname{sgn} x'(t))' = q(t)|x(g(t))|^\alpha \operatorname{sgn} x(g(t)), \alpha > 0, g(t) < t $$ and obtain a necessary and sufficient condition to possess a slowly varying solution and a regularly varying solution of index 1 at the same time.

Interval criteria for oscillation of second-order functional differential equations

By using averaging functions, new interval oscillation criteria are established for the second-order functional differential equation, ( r ( t ) | x ′ ( t ) | α − 1 x ′ ( t ) ) ′ + F ( t , x ( t ) , x ( τ ( t ) ) , x ′ ( t ) , x ′ ( τ ( t ) ) ) = 0 , t ≥ t 0 that are different from most known ones in the sense that they are based on information only on a sequence of subintervals of [ t 0, ∞], rather than on the whole half-line. Our results can be applied to three cases: ordinary, delay, and advance differential equations. In the case of half-linear functional differential equations, our criteria implies that the τ(t) ≤ t delay and Gt( t) ≥ t advance cases do not affect the oscillation. In particular, several examples are given to illustrate the importance of our results.

Interval oscillation of second-order half-linear functional differential equations

By using an inequality due to Hardy, Littlewood and Polya and averaging functions, new interval oscillation criteria are established for the half-linear functional differential equation r(t) y ′(t) α−1y ′(t) ′+q(t) y(τ(t)) α−1y(τ(t))=0, that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [ t 0,∞), rather than on the whole half-line. Our results extend and improve some previous oscillation criteria and handle the cases which are not covered by known results and implies that the delay τ( t)= t± τ does not effect the oscillation, where τ>0 is a constant. In particular, several examples that dwell upon the sharp conditions of our results are also included.