Anna Maria Piccirillo

QUALITATIVE ANALYSIS BEHAVIOUR OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL SYSTEMS

By using two-parametric scale of increasing functions the qualitative analysis of the behaviour of nonlinear impulsive differential systems solutions are investigated.

Impulsive Wendroff's type inequalities and their applications

Integro-sum inequalities for functions of two independent variables are investigated. New analogies of Wendroffs type inequalities for discontinuous functions are obtained. As applications, some hyperbolic equations with impulse influence are considered. New conditions of boundedness of solutions are obtained.

On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for Discontinuous Functions and Their Applications

We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions (integro-sum inequalities; impulse integral inequalities). Some applications of the results are included: conditions of boundedness (uniformly), stability by Lyapunov (uniformly), practical stability by Chetaev (uniformly) for the solutions of impulsive differential and integro-differential systems of ordinary differential equations.

Blow-up results for some nonlinear hyperbolic problems

Abstract We study the non-existence of global solutions for equations and inequalities of the following type ∂ttu ≥ ΔA(x, t, u) + B(x, t, u) on RN+1 + with nonlinearity A and B of the form A(x, t, u) = ρ1(x, t)|u|p , B(x, t, u) = ρ2(x, t)|u|q. We also study the nonexistence for some more general inequalities of second order but without any assumption about the type of operator. The method relies on a suitable choice of test functions, resealing techniques and a dimensional analysis.

C0,1-regularity for solution of variational inequality governed by two second order elliptic operators

Abstract The solution of a second order elliptic variational inequality is settled to be a Lipschitzian one.

Existence theorems for two classes of second order evolution variational inequalities

Abstract We prove existence theorems for the solution of two evolution unilateral second order problems, one Cauchy problem and the other periodic problem.

On a Second Order Non-linear Evolutive Equation related to a class of Dynamical Contact Problems

Abstract Existence, uniqueness and regularity properties of solution for the Cauchy problem related to a second order non-linear evolutive equation are proved.