We establish new Kamenev-type oscillation criteria for the half-linear partial differential equationunder quite general conditions. These results are extensions of the recent results developed by Sun [Y.G. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math.Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations.

We study the existence and uniqueness of nontrivial solutions for a class of fractional differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.

In this article, we investigate the uniqueness of solutions for the fractional order differential equation

Abstract. By using averaging function and the approach developed by Philos and Kong, Kamenevtype and interval oscillation criteria are established for the even order differential equation with distributed deviating arguments,The obtained results are extensions of existing ones for second order linear differential equations.Mathematics subject classification (2010): 34C10, 34C15. Keywords and phrases: oscillation, differential equations, distributed deviating arguments, even order.

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