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1

Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation

Graef J. R., Tunc E., Grace S. R.

Opuscula Mathematica

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2017

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Vol. 37, no. 6

839--852

EN

This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.

2

Oscillation of second order difference equation with a sub-linear neutral term

Dharuman C., Graef J. R., Thandapani E., Vidhyaa K. S.

Journal of Mathematics and Applications

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2017

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Vol. 40

59--67

EN

This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.

3

Uniqueness and parameter dependence of positive doubly periodic solutions of nonlinear telegraph equations

Graef J. R., Kong L., Wang M.

Opuscula Mathematica

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2014

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Vol. 34, no. 2

363--373

EN

The authors study a type of second order nonlinear telegraph equation. The existence and uniqueness of positive doubly periodic solutions are discussed. The parametric dependence of the solutions is also investigated. Two examples are given as applications of the results.

4

Multiple solutions for systems of multi-point boundary value problems

Graef J. R., Heidarkhani S., Kong L.

Opuscula Mathematica

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2013

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Vol. 33, no. 2

293--306

EN

In this paper, we establish the existence of at least three solutions of the multi-point boundary value system [formula]. The approaches used are based on variational methods and critical point theory.

5

Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations

Graef J. R., Thandapani E.

Fasciculi Mathematici

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2001

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Nr 31

23-36

EN

The authors consider the nonlinear difference equation (E) delta2 ((delta(bn delta yn))+f(n,yn-t)=0, n należy N(no)={no,no+1,...}, here {an} and {bn} are positive real sequences, I is a nonnegative integer, f: N(no) x R R is a continuous function with uf(n, u) > 0 for all u nierówne 0. They obtain necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior. They also obtain sufficient conditions for all solutions to be oscillatory if/ is either strongly sublinear or strongly superlinear. Examples of their results are also included.