Giuseppe Caristi

Mathematical Programming with (Φ, ρ)-invexity

We introduce new invexity-type properties for differentiable functions, generalizing (F, ρ)-convexity. Optimality conditions for nonlinear programming problems are established under such assumptions, extending previously known results. Wolfe and Mond-Weir duals are also considered, and we obtain direct and converse duality theorems.

Infinitely many solutions for perturbed impulsive fractional differential systems

In this paper, the existence of infinitely many solutions for perturbed systems of impulsive non-linear fractional differential equations including Lipschitz continuous non-linear terms is discussed. The approach is based on variational methods. In addition, examples are presented to illustrate the feasibility and effectiveness of the main results.

Variational approaches to p-Laplacian discrete problems of Kirchhoff-type

Abstract Critical point results for Kirchhoff-type discrete boundary value problems are exploited in order to prove that a suitable class possesses at least one solution under an asymptotical behaviour of the potential of the nonlinear term at zero, and also possesses infinitely many solutions under some hypotheses on the behaviour of the potential of the nonlinear term at infinity. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.

Multiplicity results for p(x)-biharmonic equations with Navier boundary conditions

This paper deals with the existence of solutions for a class of p(x)-biharmonic equations with Navier boundary conditions. The approach is based on variational methods and critical point theory. Indeed, we investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Moreover, by combining two algebraic conditions on the nonlinear term which guarantee the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of the third solution for the problem.

A variational approach to difference equations

In this paper, we are concerned with the existence of at least three distinct solutions for nonlinear difference equations with Dirichlet boundary conditions. The proof of the main result is based on variational methods. We also provide an example in order to illustrate the main results.

New Invexity-Type Conditions in Constrained Optimization

In the present paper we define weaker invexity-type properties and examine the relationships between the new concepts and other similar conditions. One obtains in this way necessary and sufficient conditions for Kuhn-Tucker sufficiency. Moreover one proves that the same conditions are sufficient for Wolfe duality.

On gap functions for nonsmooth multiobjective optimization problems

A set-valued gap function,

An Existence Result for Impulsive Multi-point Boundary Value Systems Using a Local Minimization Principle

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