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19: Paper Source PDF document

Paper's Title:

On Oscillation of Second-Order Delay Dynamic Equations on Time Scales


S. H. Saker

Department of Mathematics, Faculty of Science,
Mansoura University, Mansoura, 35516,


Some new oscillation criteria for second-order linear delay dynamic equation on a time scale T are established. Our results improve the recent results for delay dynamic equations and in the special case when T=R, the results include the oscillation results established by Hille [1948, Trans. Amer. Math. Soc. 64 (1948), 234-252] and Erbe [Canad. Math. Bull. 16 (1973), 49-56.] for differential equations. When T=Z the results include and improve some oscillation criteria for difference equations. When T=hZ, h>0, T=qN and T=N2, i.e., for generalized second order delay difference equations our results are essentially new and can be applied on different types of time scales. An example is considered to illustrate the main results.

4: Paper Source PDF document

Paper's Title:

On the Biharmonic Equation with Nonlinear Boundary Integral Conditions


R. Hamdouche and H. Saker

L.M.A. Department of Mathematics, Faculty of Sciences,
University of Badji Mokhtar,
P.O.Box 12. Annaba 23000,



In the present work, we deal with the biharmonic problems in a bounded domain in the plane with the nonlinear boundary integral conditions. After applying the Boundary integral method, a system of nonlinear boundary integral equations is obtained. The result show that when the nonlinearity satisfies some conditions lead the existence and uniqueness of the solution.

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