A boundary value problem of fractional order at resonance.
A certain type of partial differential equations on tori
The existence of classical solutions for some partial differential equations on tori is shown.
A characterization of the essential spectrum and applications
In this article the essential spectrum of closed, densely defined linear operators is characterized on a large class of spaces, which possess the Dunford-Pettis property or which isomorphic to one of the spaces . A practical...
A class of retracts in with some applications to differential inclusion
A class of singular fourth-order boundary value problems with nonhomogeneous nonlinearity
We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.
A complement to the Fredholm theory of elliptic systems on bounded domains.
A discrete contact model for crowd motion
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the...
A discrete contact model for crowd motion
The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here...
A family of Lyapunov-based control schemes for maximum power point tracking in buck converters
This paper presents a novel family of Lyapunov-based controllers for the maximum power point tracking problem in the buck converter case. The solar power generation system here considered is composed by a stand-alone photovoltaic panel connected to a DC/DC buck converter. Lyapunov function candidates depending on the output are considered to develop conditions which, in some cases, can be expressed as linear matrix inequalities; these conditions guarantee that the output goes asymptotically to zero,...
A fast numerical test of multivariate polynomial positiveness with applications
The paper presents a simple method to check a positiveness of symmetric multivariate polynomials on the unit multi-circle. The method is based on the sampling polynomials using the fast Fourier transform. The algorithm is described and its possible applications are proposed. One of the aims of the paper is to show that presented algorithm is significantly faster than commonly used method based on the semi-definite programming expression.
A fixed point approach to the stability of differential equations .
A fixed Point Theorem and its Applications to Nonlinear Integral Equations in Banach Algebras
A fourth-order boundary value problem with one-sided Nagumo condition.
A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.
A generalized Amman's fixed point theorem and its application to Nash equlibrium.
A geometrical property of causal invertible systems.
A global description of solutions to nonlinear perturbations of the Wiener--Hopf integral equations.
A hybrid method for monotone variational inequalities involving pseudocontractions.
A mathematical introduction to the Wigner formulation of quantum mechanics
The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of the Wigner transform and eventually deduce the Wigner equation.
A minimax inequality with applications to existence of equilibrium point and fixed point theorems
Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an...