Upper and lower solutions method and a fractional differential equation boundary value problem.
Upper and lower solutions satisfying the inverse inequality
We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.
Variational methods for boundary value problems.
Various half-eigenvalues of scalar -Laplacian with indefinite integrable weights.
Verification of functional a posteriori error estimates for obstacle problem in 1D
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
Verification of functional a posteriori error estimates for obstacle problem in 2D
We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value...
Volume Filling Effect in Modelling Chemotaxis
The oriented movement of biological cells or organisms in response to a chemical gradient is called chemotaxis. The most interesting situation related to self-organization phenomenon takes place when the cells detect and response to a chemical which is secreted by themselves. Since pioneering works of Patlak (1953) and Keller and Segel (1970) many particularized models have been proposed to describe the aggregation phase of this process. Most of...
Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces.
Weak solutions of a boundary value problem for nonlinear ordinary differential equation of second order in Banach spaces
Zero convergent solutions for a class of -Laplacian systems
Zeros of derivatives of solutions to singular conjugate BVPs
Positive solutions of the singular conjugate BVP are studied. The set of all zeros of their derivatives up to order is described. By means of this, estimates from below of the solutions and the absolute values of their derivatives up to order on the considered interval are reached. Such estimates are necessary for the application of the general existence principle to the BVP under consideration.
-Laplacian BVPs with linear bounded operator conditions
The aim of this paper is to present new existence results for -Laplacian boundary value problems with linear bounded operator conditions. Existence theorems are obtained using the Schauder and the Krasnosel’skii fixed point theorems. Some examples illustrate the results obtained and applications to multi-point boundary value problems are provided.
Заметка о разрешимости некоторых краевых задач для обыкновенного дифференциального уравнения -го порядка
Исследование сходимости интерационного процесса для решения одной стационарной задачи теории мягких оболочек
Критерии однозначной разрешимости двухточечных краевых задач с обыкновенным дифференциальным уравнением n-го порядка
Метод конечных разностей решения первой краевой задачи для нелинейного обыкновенного дифференциального уравнения второго порядка с дивергентной главной частью
Новые априорные оценки решений двухточечной краевой задачи и их приложения
О краевых задачах для систем обыкновенных дифференциальных уравнений 2-го порядка
Об одной задаче с интегральными условиями для системы обыкновенных дифференциальных уравнений
Об одной краевой задаче на незакрепленном отрезке.