A multidimensional optimization problem is considered, which is formulated in terms of tropical mathematics as to minimize a nonlinear objective function subject to linear inequality constraints. The optimization problem is motivated by a problem in project scheduling when an optimal schedule is given by minimizing the flow time of activities in a project under various activity precedence const...

This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations. 1. Introduction. It is well known that integral inequalities play a very crucial role in the stud...

We discuss a nonlinear beam obstacle model defined by inequality constraints and differential equations with highly nonlinear and fourth order operators. An appropriate discrete approximation by the finite element method leads to a large finite-dimensional mixed nonlinear complementarity problem. We propose an interior-point algorithm for the solution of this complementarity problem. Some compu...

From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality (cf. [1–9, 11–17]). However, for the nth-order nonlinear differential equations with the nonlinear boundary conditions, results are very few. The authors made some attempts to solve the nth-order Robin problem [14]. Now ...

In this article we derive a generalized version of nonlinear Picone’s identity for the p-Laplacian. We use this identity to obtain a Hardy-type inequality and a Sturm comparison result. We also establish the relationship between the components of the solution of nonlinear elliptic systems.

In this work, some new interval oscillation criteria for solutions of a class of nonlinear fractional differential equations are established by using a generalized Riccati function and inequality technique. For illustrating the validity of the established results, we also present some applications for them. Key–Words: Oscillation; Interval criteria; Qualitative properties; Fractional differenti...

In this paper, we address the problem of designing nonlinear observers for dynamical discretetime systems with both constant and time-varying delay nonlinearities. The nonlinear system is assumed to verify the usual Lipschitz condition that permits us to transform the nonlinear system into a linear time-delay system with structured uncertainties. The existence of the observer-gain is ensured by...

We introduce and study a new class of generalized nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of generalized nonlinear variational-like inequalities. A new iterative algorithm for finding the approximate solutions of the generalized nonlinear variational-like inequality is given and the convergence of the algorithm is als...

Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. The results are illustrated b...

In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results. Keywords—Discrete-time SIR epidemic model, Time delay, Nonlinear incidence rat...