A partial generalization of Diliberto’s theorem for certain DEs of higher dimension
A partially ordered space connected with the de la Vallée Poussin problem
A particular solution of a Painlevé system in terms of the hypergeometric function .
A periodic boundary value problem in Hilbert space
In the paper some existence results for periodic boundary value problems for the ordinary differential equation of the second order in a Hilbert space are given. Under some auxiliary assumptions the set of solutions is compact and connected or it is convex.
A Periodic Lotka-Volterra System
In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters.
A periodic model for the dynamics of cell volume
We prove the existence and uniqueness of a positive periodic solution for a model describing the dynamics of cell volume flux, introduced by Julio A. Hernández [Bull. Math. Biol. 69 (2007), 1631-1648]. We also show that the periodic solution is a global attractor. Our results confirm the conjectures made in an interesting recent book of P. J. Torres [Atlantis Press, 2015].
A Perron-type theorem for nonautonomous delay equations
We show that if the Lyapunov exponents of a linear delay equation x′ = L(t)x t are limits, then the same happens with the exponential growth rates of the solutions to the equation x′ = L(t)x t + f(t, x t) for any sufficiently small perturbation f.
A perspective on the contributions of Alan C. Lazer to critical point theory.
A perturbation-based model for rectifier circuits.
A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
A phase of the differential equation with a complex coefficient of the real variable
A Picard method without Lipschitz continuity for some ordinary differential equations
A Picone type identity for second-order half-linear differential equations.
A polar coordinate transformation for nonhomogeneous differential systems
A pole assignment technique for multivariable systems with input delay
A polynomial class of Markus-Yamabe counterexamples.
In the paper [CEGHM] a polynomial counterexample to the Markus-Yamabe Conjecture and to the discrete Markus-Yamabe Question in dimension n ≥ 3 are given. In the present paper we explain a way for obtaining a family of polynomial counterexamples containing the above ones. Finally we study the global dynamics of the examples given in [CEGHM].
A positive solution for singular discrete boundary value problems with sign-changing nonlinearities.
A Poster about the Old History of Fractional Calculus
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.
A Poster about the Recent History of Fractional Calculus
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.
A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
FEM discretizations of arbitrary order are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.