Displaying similar documents to “Exact Solutions of Nonlocal Pluriparabolic Problems”

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

Similarity:

We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

Dimovski, Ivan, Tsankov, Yulian (2012)

Mathematica Balkanica New Series

Similarity:

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05 In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::;...

On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions

Aris Tersenov (2001)

Annales Polonici Mathematici

Similarity:

This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.

Functions uniformly quiet at zero and existence results for one-parameter boundary value problems

G. L. Karakostas, P. Ch. Tsamatos (2002)

Annales Polonici Mathematici

Similarity:

We introduce the notion of uniform quietness at zero for a real-valued function and we study one-parameter nonlocal boundary value problems for second order differential equations involving such functions. By using the Krasnosel'skiĭ fixed point theorem in a cone, we give values of the parameter for which the problems have at least two positive solutions.

Three-Dimensional Operational Calculi for Nonlocal Evolution Boundary Value Problems Тримерни операционни смятания за нелокални еволюционни гранични задачи

Dimovski, Ivan, Tsankov, Yulian (2011)

Union of Bulgarian Mathematicians

Similarity:

Иван Христов Димовски, Юлиан Цанков Цанков - Построени са директни операционни смятания за функции u(x, y, t), непрекъснати в област от вида D = [0, a] × [0, b] × [0, ∞). Наред с класическата дюамелова конволюция, построението използва и две некласически конволюции за операторите ∂2x и ∂2y. Тези три едномерни конволюции се комбинират в една тримерна конволюция u ∗ v в C(D). Вместо подхода на Я. Микусински, основаващ се на конволюционни частни, се развива алтернативен подход с използване...

Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane

Antonio Greco, Giuseppe Viglialoro (2023)

Applications of Mathematics

Similarity:

This paper deals with a mixed boundary-value problem of Ventcel type in two variables. The peculiarity of the Ventcel problem lies in the fact that one of the boundary conditions involves second order differentiation along the boundary. Under suitable assumptions on the data, we first give the definition of a weak solution, and then we prove that the problem is uniquely solvable. We also consider a particular case arising in real-world applications and discuss the resulting model. ...

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation Точни решения на нелокални гранични задачи за едно- и двумерни уравнения на топлопроводноста

Dimovski, Ivan, Tsankov, Yulian (2012)

Union of Bulgarian Mathematicians

Similarity:

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи...

Systems of differential inclusions in the absence of maximum principles and growth conditions

Christopher C. Tisdell (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to...

The transmission problem with boundary conditions given by real measures

Dagmar Medková (2007)

Annales Polonici Mathematici

Similarity:

The unique solvability of the problem Δu = 0 in G⁺ ∪ G¯, u₊ - au_ = f on ∂G⁺, n⁺·∇u₊ - bn⁺·∇u_ = g on ∂G⁺ is proved. Here a, b are positive constants and g is a real measure. The solution is constructed using the boundary integral equation method.