İmpalsif diferansiyel denklemlerde sturm karşılaştırma teorileri.

In this thesis, we investigate Sturmian comparison theory and oscillation for second order impulsive differential equations with fixed moments of impulse actions. It is shown that impulse actions may greatly alter the oscillation behavior of solutions. In chapter two, besides Sturmian type comparison results, we give Leightonian type comparison theorems and obtain Wirtinger type inequalities for linear, half-linear and non-selfadjoint equations. We present analogous results for forced super linear and super half-linear equations with damping. In chapter three, we derive sufficient conditions for oscillation of nonlinear equations. Integral averaging, function averaging techniques as well as interval criteria for oscillation are discussed. Oscillation criteria for solutions of impulsive Hill̕s equation with damping and forced linear equations with damping are established.Ph.D. - Doctoral Progra

Forced Oscillation of Second-Order Impulsive Differential Equations with Mixed Nonlinearities

In this paper we give new oscillation criteria for a class of second-order mixed nonlinear impulsive differential equations having fixed moments of impulse actions. The method is based on the existence of a nonprincipal solution of a related second-order linear homogeneous equation

Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations

New oscillation criteria are obtained for second order forced mixed nonlinear impulsive differential equations of the for

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

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

In this paper, we give a nonoscillation criterion for half-linear equations with periodic coefficients under fixed moments of impulse actions. The method is based on the existence of positive solutions of the related Riccati equation and a recently obtained comparison principle. In the special case when the equation becomes impulsive Hill equation new oscillation criteria are also obtained

SECOND ORDER OSCILLATION OF MIXED NONLINEAR DYNAMIC EQUATIONS WITH SEVERAL POSITIVE AND NEGATIVE COEFFICIENTS

New oscillation criteria are obtained for superlinear and sublinear forced dynamic equations having positive and negative coefficients by means of nonprincipal solutions

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

New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations with Nonlinear Neutral Terms

In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples

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

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