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.
A predator-prey Gompertz model with time delay and impulsive perturbations on the prey.
A predator-prey model in the chemostat with time delay.
A predator-prey model with state dependent impulsive effects
We investigate a Lotka-Volterra predator-prey model with state dependent impulsive effects, in which the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. We present some sufficient conditions to guarantee the existence and asymptotical stability of semi-trivial periodic solutions and positive periodic solutions.
A predictive method allowing the use of a single ionic model in numerical cardiac electrophysiology
One of the current debate about simulating the electrical activity in the heart is the following: Using a realistic anatomical setting, i.e. realistic geometries, fibres orientations, etc., is it enough to use a simplified 2-variable phenomenological model to reproduce the main characteristics of the cardiac action potential propagation, and in what sense is it sufficient? Using a combination of dimensional and asymptotic analysis, together with the well-known Mitchell − Schaeffer model, it is shown...
A prey-predator model with a cover linearly varying with the prey population and an alternative food for the predator.
A prey-predator model with an alternative food for the predator, harvesting of both the species and with a gestation period for interaction.
A principle of linearization in theory of stability of solutions of variational inequalities
It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
A priori bounds for a semilinear wave equation
A priori estimates and solvability of a non-resonant generalized multi-point boundary value problem of mixed Dirichlet-Neumann-Dirichlet type involving a -Laplacian type operator
This paper is devoted to the problem of existence of a solution for a non-resonant, non-linear generalized multi-point boundary value problem on the interval . The existence of a solution is obtained using topological degree and some a priori estimates for functions satisfying the boundary conditions specified in the problem.
A priori estimates for solutions to a four point boundary value problem for singularly perturbed semilinear differential equations.
A priori estimates for the existence of a solution for a multi-point boundary value problem.
A probabilistic and geometric perspective.
A problem on the zeros of the Mittag-Leffler function and the spectrum of a fractional-order differential operator.
A procedure for the solution of the equations of motion by the finite element method
A proof existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems.
A proof of monotony of the Temple quotients in eigenvalue problems
If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue , the sequences of the so-called Schwarz quatients (which are upper bounds for ) and of the so-called Temple quotients (which are lower bounds) are constructed. While monotony of the first sequence was proved many years ago, monotony of the second one has been proved only recently by F. goerisch and J. Albrecht in their common paper “Die Monotonie der Templeschen Quotienten” (ZAMM, in print). In the present...