Existence of Solutions for Cauchy Problems and Periodic Problems with Multivalued Pseudo Monotone Operators

2000 ◽  
pp. 273-286
Author(s):  
Naoki Shioji
Keyword(s):  
Existence Of Solutions ◽  
Monotone Operators ◽  
Cauchy Problems ◽  
Periodic Problems

scholarly journals A class of nonlinear elliptic problems with nonconvex constraints and applications

1998 ◽  
Vol 41 (2) ◽  
pp. 333-357
Author(s):  
N. Chemetov ◽  
J. F. Rodrigues
Keyword(s):  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Monotone Operators ◽  
Global Constraints ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Biological Population ◽  
Unilateral Problems ◽  
Nonlocal Terms ◽  
Nonconvex Constraints

Conditions for the existence of solutions of a class of elliptic problems with nonconvex constraints are given in the general framework of pseudo-monotone operators. Applications are considered in unilateral problems of free boundary type, yielding the solvability of a Reynold's lubrication model and of a biological population problem with nonlocal terms and global constraints.

scholarly journals Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 55
Author(s):  
Valeria Marraffa ◽  
Bianca Satco
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Compact Convex ◽  
Upper Semicontinuity ◽  
Periodic Boundary Conditions ◽  
Set Valued Mapping ◽  
Periodic Problems ◽  
The Right

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions.

scholarly journals Existence and Stability of Iterative Algorithm for a System of Random Set-Valued Variational Inclusion Problems Involving (A,m,η)-Generalized Monotone Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Jittiporn Suwannawit ◽  
Narin Petrot
Keyword(s):  
Iterative Algorithm ◽  
Monotone Operator ◽  
Existence Of Solutions ◽  
Monotone Operators ◽  
Variational Inclusion ◽  
Random Set ◽  
Inclusion Problems ◽  
Existence And Stability ◽  
The Stability

We introduce and study a class of a system of random set-valued variational inclusion problems. Some conditions for the existence of solutions of such problems are provided, when the operators are contained in the classes of generalized monotone operators, so-called (A,m,η)-monotone operator. Further, the stability of the iterative algorithm for finding a solution of the considered problem is also discussed.

scholarly journals Bounded solutions of nonlinear Cauchy problems

2002 ◽  
Vol 7 (12) ◽  
pp. 637-661 ◽  
Author(s):  
Josef Kreulich
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Existence Of Solutions ◽  
Continuous Functions ◽  
Almost Periodicity ◽  
Cauchy Problems ◽  
Bounded Solutions ◽  
Translation Invariant ◽  
Uniformly Continuous ◽  
Translation Invariant Subspace

For a given closed and translation invariant subspaceYof the bounded and uniformly continuous functions, we will give criteria for the existence of solutionsu∈Yto the equationu′(t)+A(u(t))+ωu(t)∍f(t),t∈ℝ, or of solutionsuasymptotically close toYfor the inhomogeneous differential equationu′(t)+A(u(t))+ωu(t)∍f(t),t>0,u(0)=u0, in general Banach spaces, whereAdenotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the spaceYare spaces of functions with various almost periodicity properties and more general types of asymptotic behavior.

scholarly journals A remark on a theorem of Browder

2013 ◽  
Vol 29 (1) ◽  
pp. 119-123
Author(s):  
CORNELIU UDREA ◽  
Keyword(s):  
Banach Space ◽  
Convex Sets ◽  
Existence Of Solutions ◽  
Type Theorem ◽  
Monotone Operators ◽  
Dual Pair ◽  
Normed Spaces ◽  
Browder’S Theorem ◽  
Weakly Continuous ◽  
Weakly Closed

This work deals with a Browder type theorem, and some of its consequences.We consider hX, Y i a dual pair of real normed spaces, C a weakly closed convex subset of X containing 0X, and L a function from C into Y which is monotone, weakly continuous on the line segments in C, and coercive. In the article ,,Nonlinear monotone operators and convex sets in Banach spaces”, Bull. Amer. Math. Soc., 71 (1965), F. E. Browder proved the existence of solutions for variational inequalities with such an operator L provided that X = E is a reflexive Banach space, and Y = E0 is its dual space. It is the object of this note to remark that a similar result is valid when Y = E is a Banach space (not necessary reflexive) and X = E0 (for example in the case of the Lebesgue spaces E = L1 (T), and E0 = L∞(T)). Moreover we shall show that the Browder’s theorem is a consequence of this result, and we shall also prove a Stampacchia type theorem.

scholarly journals Fuzzy Fixed Point Results in F-Metric Spaces with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cauchy Problems ◽  
Research Directions ◽  
New Research ◽  
Fuzzy Fixed Point

In this paper, some concepts of F-metric spaces are used to study a few fuzzy fixed point theorems. Consequently, corresponding fixed point theorems of multivalued and single-valued mappings are discussed. Moreover, one of our obtained results is applied to establish some conditions for existence of solutions of fuzzy Cauchy problems. It is hoped that the established ideas in this work will awake new research directions in fuzzy fixed point theory and related hybrid models in the framework of F-metric spaces.

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