In this article, we establish new Lyapunov-type inequalities for third-order linear differential equations y′′′ + q(t)y = 0 under the three-point boundary conditions y(a) = y(b) = y(c) = 0 and y(a) = y′′(d) = y(b) = 0 by bounding Green’s functions G(t, s) corresponding to appropriate boundary conditions. Thus, we obtain the best constants of Lyapunov-type inequalities for three-point boundary v...

In this paper, some fundamental strict and non-strict differential inequalities for the implicit perturbations of nonlinear first order ordinary causal differential equations have been established.

In this paper we study the following problem: Given that certain functionals of u and its derivatives belong to given Lclasses over the infinite interval, what can be said about the L-classes of other functionals? Utilizing a simple device from the theory of linear differential equations, we obtain a number of results due to Landau, Kolmogoroff, Halperin-von Neumann, and Nagy, together with som...

Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan 2003 and Pachpatte 2004 . These inequalities can be used as basic tools in the study of certain classes of functional differential equations as well as integral equations. A existence and a uniqueness on the solution of the functional differential equation involving...

Some variants of one-dimensional and two-dimensional integral inequalities of the Volterra type are applied to study the behaviour properties of the solutions to various boundary value problems for partial differential equations of the hyperbolic type. Moreover, new types of integral inequalities for one and two variables, being a generalization of the Gronwall inequality, are presented and use...

Using the “basic monotonicity property” along locally admissible trajectories, we extend to very general problems certain existing results concerning the differential inequalities verified by the value function of an optimal control problem; these differential inequalities are expressed in terms of its contingent, quasitangent, and peritangent (Clarke’s) directional derivatives and in terms of ...