scholarly journals Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators

2020 ◽  
Vol 187 (2) ◽  
pp. 391-407
Author(s):  
Dumitru Motreanu ◽  
Van Thien Nguyen ◽  
Shengda Zeng
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Nonsmooth Analysis ◽  
Obstacle Problem ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Obstacle Problems ◽  
Generalized Gradient ◽  
Fixed Point Principle ◽  
Set Valued Mappings

Abstract The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis.

scholarly journals Existence results for double phase implicit obstacle problems involving multivalued operators

2020 ◽  
Vol 59 (5) ◽  
Author(s):  
Shengda Zeng ◽  
Yunru Bai ◽  
Leszek Gasiński ◽  
Patrick Winkert
Keyword(s):  
Nonsmooth Analysis ◽  
Existence Results ◽  
Obstacle Problems ◽  
Multivalued Mappings ◽  
Phase Operator ◽  
Generalized Gradient ◽  
Double Phase ◽  
Fixed Point Principle ◽  
Multivalued Operators ◽  
Gradient Based

Abstract In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence of at least one solution.

scholarly journals Existence of solutions for generalized nonlinear vector quasi-variational-like inequalities with set-valued mappings

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 909-916 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Set Valued Mappings ◽  
Nonlinear Vector ◽  
Locally Convex

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variational- like inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalized mixed quasi-variational-like inequalities and so on. By means of fixed point theorem, we obtain existence theorem of solutions to the class of generalized nonlinear vector quasi-variational-like inequalities in the setting of locally convex topological vector spaces.

scholarly journals An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions

This paper studies the existence of solutions for a boundary value problem of nonlinear fractional hybrid differential inclusions by using a fixed point theorem due to Dhage (2006). The main result is illustrated with the aid of an example.

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

scholarly journals An existence theorem for nonlinear delay differential equations

1989 ◽  
Vol 2 (2) ◽  
pp. 85-89
Author(s):  
Krishnan Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

In this paper we prove a theorem on the existence of solutions of nonlinear delay differential equations, with implicit derivatives. The result is established using the measure of noncompactness of a set and Darbo's fixed point theorem.

scholarly journals Solvability of Some Boundary Value Problems for Fractional -Laplacian Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Taiyong Chen ◽  
Wenbin Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Growth Conditions ◽  
Existence Results ◽  
Laplacian Equation ◽  
Nonlinear Growth

This paper considers the existence of solutions for two boundary value problems for fractional -Laplacian equation. Under certain nonlinear growth conditions of the nonlinearity, two new existence results are obtained by using Schaefer's fixed point theorem. As an application, an example to illustrate our results is given.

scholarly journals A System of Generalized Variational-Hemivariational Inequalities with Set-Valued Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhi-bin Liu ◽  
Jian-hong Gou ◽  
Yi-bin Xiao ◽  
Xue-song Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Theorem ◽  
Point Theorem ◽  
Directional Derivatives ◽  
Hemivariational Inequalities ◽  
Kkm Theorem ◽  
Special Cases ◽  
Generalized Directional Derivatives ◽  
Set Valued Mappings

By using surjectivity theorem of pseudomonotone and coercive operators rather than the KKM theorem and fixed point theorem used in recent literatures, we obtain some conditions under which a system of generalized variational-hemivariational inequalities concerning set-valued mappings, which includes as special cases many problems of hemivariational inequalities studied in recent literatures, is solvable. As an application, we prove an existence theorem of solutions for a system of generalized variational-hemivariational inequalities involving integrals of Clarke's generalized directional derivatives.

scholarly journals Convergence rates for the classical, thin and fractional elliptic obstacle problems

2015 ◽  
Vol 373 (2050) ◽  
pp. 20140449 ◽  
Author(s):  
Ricardo H. Nochetto ◽  
Enrique Otárola ◽  
Abner J. Salgado
Keyword(s):  
Obstacle Problem ◽  
Fractional Laplacian ◽  
Convergence Rates ◽  
Finite Element Approximation ◽  
Obstacle Problems ◽  
Element Approximation ◽  
Optimal Error ◽  
Optimal Convergence Rates ◽  
Regularity Results ◽  
Thin Obstacle

We review the finite-element approximation of the classical obstacle problem in energy and max-norms and derive error estimates for both the solution and the free boundary. On the basis of recent regularity results, we present an optimal error analysis for the thin obstacle problem. Finally, we discuss the localization of the obstacle problem for the fractional Laplacian and prove quasi-optimal convergence rates.

scholarly journals Approximating Fixed Points of The General Asymptotic Set Valued Mappings

2020 ◽  
Vol 18 ◽  
pp. 52-59
Author(s):  
Salwa Salman Abed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Reflexive Banach Spaces ◽  
Set Valued Mapping ◽  
Set Valued Mappings ◽  
Fixed Point Iterative Method

  The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping  and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by  yn+1 = tn z+ (1-tn )un ,  un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces.  As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved

scholarly journals Existence of solutions of a special class of fuzzy integral equations

2006 ◽  
Vol 2006 ◽  
pp. 1-8
Author(s):  
K. Balachandran ◽  
K. Kanagarajan
Keyword(s):  
Existence Theorem ◽  
Integral Equations ◽  
Fuzzy Set ◽  
Special Class ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Fuzzy Integral ◽  
Set Valued Mappings

We prove an existence theorem for a special class of fuzzy integral equations involving fuzzy set-valued mappings. The results are obtained by using the contraction mapping principle.

Sign in / Sign up

Export Citation Format

Share Document