scholarly journals On a solution of monotone type problems with uncertain inputs

2011 ◽  
Vol 48 (1) ◽  
pp. 145-152
Author(s):  
Luděk Nechvátal
Keyword(s):  
Type Problem ◽  
Existence Of A Solution ◽  
Scenario Method ◽  
Monotone Type

Abstract The paper deals with a nonlinear weak monotone type problem and its solution with respect to uncertain coefficients in the equation. The so- -called worst scenario method is adopted. The formulation of suitable conditions and a proof of the existence of a solution of the worst scenario problem is presented.

scholarly journals Nonlinear periodic parabolic problems with nonmonotone discontinuities

1998 ◽  
Vol 41 (1) ◽  
pp. 117-132
Author(s):  
Dimitrios A. Kandilakis ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Lower Solution ◽  
Parabolic Problems ◽  
Order Interval ◽  
Existence Of A Solution ◽  
Parabolic Boundary ◽  
Upper And Lower Solution ◽  
Monotone Type

In this paper we consider a nonlinear periodic parabolic boundary value problem with a discontinuous nonmonotone nonlinearity. Using a lifting result for operators of type (S+), a general surjectivity theorem for operators of monotone type and an auxiliary problem defined by truncation and penalization we prove the existence of a solution in the order interval formed by an upper and lower solution. Moreover we show that the set of all such solutions is compact in Lp(T, (Z)).

scholarly journals On a nonlocal boundary value problem with an oblique derivative

2020 ◽  
Vol 22 (1) ◽  
pp. 81-93
Author(s):  
Kulzina Zh. Nazarova ◽  
Batirkhan Kh. Turmetov ◽  
Kairat Id. Usmanov
Keyword(s):  
Boundary Value Problem ◽  
Laplace Equation ◽  
Nonlocal Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Type Problem ◽  
Nonlocal Boundary Value Problem ◽  
Existence Of A Solution ◽  
Dirichlet Type ◽  
Dirichlet Type Problem

The work studies the solvability of a nonlocal boundary value problem for the Laplace equation. The nonlocal condition is introduced using transformations in the Rn space carried out by some orthogonal matrices. Examples and properties of such matrices are given. To study the main problem, an auxiliary nonlocal Dirichlet-type problem for the Laplace equation is first solved. This problem is reduced to a vector equation whose elements are the solutions of the classical Dirichlet probem. Under certain conditions for the boundary condition coefficients, theorems on uniqueness and existence of a solution to a problem of Dirichlet type are proved. For this solution an integral representation is also obtained, which is a generalization of the classical Poisson integral. Further, the main problem is reduced to solving a non-local Dirichlet-type problem. Theorems on existence and uniqueness of a solution to the problem under consideration are proved. Using well-known statements about solutions of a boundary value problem with an oblique derivative for the classical Laplace equation, exact orders of smoothness of a problem's solution are found. Examples are also given of the cases where the theorem conditions are not fulfilled. In these cases the solution is not unique.

scholarly journals Homogenization of monotone type problems with uncertain data

2009 ◽  
Vol 43 (1) ◽  
pp. 163-171
Author(s):  
Luděk Nechvátal
Keyword(s):  
Differential Operators ◽  
Uncertain Data ◽  
Deterministic Approach ◽  
Nonlinear Differential Operators ◽  
Scenario Method ◽  
Monotone Type

Abstract The paper deals with homogenization of nonlinear differential operators with monotone behaviour. We consider a situation, when the coefficients of the operator are not known exactly, but in certain bounds only due to errors caused by measurements. We use the deterministic approach to the problem- -worst scenario method introduced by I. Hlaváček.

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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