Abdullah Özbekler

Interval criteria for the forced oscillation of super-half-linear differential equations under impulse effects

In this paper, we derive new interval oscillation criteria for a forced super-half-linear impulsive differential equation having fixed moments of impulse actions. The results are extended to a more general class of nonlinear impulsive differential equations. Examples are also given to illustrate the relevance of the results.

Forced oscillation of super-half-linear impulsive differential equations

By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered.

Disconjugacy via Lyapunov and Vallée-Poussin type inequalities for forced differential equations

In the case of oscillatory potentials, we present some new Lyapunov and Vallee-Poussin type inequalities for second order forced differential equations. No sign restriction is imposed on the forcing term. The obtained inequalities generalize and compliment the existing results in the literature.

Principal and nonprincipal solutions of impulsive differential equations with applications

We introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results.

Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients

Abstract In this paper we give new oscillation criteria for forced super- and sub-linear differential equations by means of nonprincipal solutions.

Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives

AbstractWe state and prove new generalized Lyapunov-type and Hartman-type inequalities for a conformable boundary value problem of order α∈(1,2]

Nonoscillation and oscillation of second-order impulsive differential equations with periodic coefficients

\alpha \in (1,2]

Lyapunov type inequalities for second-order differential equations with mixed nonlinearities

with mixed non-linearities of the form (Tαax)(t)+r1(t)|x(t)|η−1x(t)+r2(t)|x(t)|δ−1x(t)=g(t),t∈(a,b),

Sturmian theory for second order differential equations with mixed nonlinearities

\bigl(\mathbf{T}_{\alpha }^{a} x\bigr) (t)+r_{1}(t) \bigl\vert x(t) \bigr\vert ^{\eta -1}x(t)+r_{2}(t)\bigl\vert x(t) \bigr\vert ^{ \delta -1}x(t)=g(t), \quad t\in (a,b),