Morse inequalities for diffeomorphisms of a compact manifold were first proved by Smale [21] under the assumption that the nonwandering set is finite. We call these the integral Morse inequalities. They were generalized by Zeeman in an unpublished work cited in [25] to diffeomorphisms with a hyperbolic chain recurrent set that is axiom-A-diffeomorphisms which satisfy the no cycle condition. For...

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...