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On solutions set of a multivalued stochastic differential equation

Marek T. MalinowskiRavi P. Agarwal — 2017

Czechoslovak Mathematical Journal

We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.

Periodicity, almost periodicity for time scales and related functions

Chao WangRavi P. AgarwalDonal O’Regan — 2016

Nonautonomous Dynamical Systems

In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

Solution to Fredholm integral inclusions via ( F, δ b )-contractions

Hemant Kumar NashineRavi P. AgarwalZoran Kadelburg — 2016

Open Mathematics

We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

Dead cores of singular Dirichlet boundary value problems with φ -Laplacian

Ravi P. AgarwalDonal O'ReganStaněk, Svatoslav — 2008

Applications of Mathematics

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem ( φ ( u ' ) ) ' = λ f ( t , u , u ' ) , u ( 0 ) = u ( T ) = A . Here λ is the positive parameter, A > 0 , f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable.

Impulsive semilinear neutral functional differential inclusions with multivalued jumps

Nadjet AbadaRavi P. AgarwalMouffak BenchohraHadda Hammouche — 2011

Applications of Mathematics

In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.

Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings

Zeqing LiuRavi P. AgarwalChi FengShin Min Kang — 2005

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results are sharp....

On the existence of multiple periodic solutions for the vector p -Laplacian via critical point theory

Haishen LüDonal O'ReganRavi P. Agarwal — 2005

Applications of Mathematics

We study the vector p -Laplacian - ( | u ' | p - 2 u ' ) ' = F ( t , u ) a.e. t [ 0 , T ] , u ( 0 ) = u ( T ) , u ' ( 0 ) = u ' ( T ) , 1 < p < . ( * ) We prove that there exists a sequence ( u n ) of solutions of ( * ) such that u n is a critical point of ϕ and another sequence ( u n * ) of solutions of ( * ) such that u n * is a local minimum point of ϕ , where ϕ is a functional defined below.

Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach

Haishen LüDonal O'ReganRavi P. Agarwal — 2007

Applications of Mathematics

This paper studies the existence of solutions to the singular boundary value problem - u ' ' = g ( t , u ) + h ( t , u ) , t ( 0 , 1 ) , u ( 0 ) = 0 = u ( 1 ) , where g ( 0 , 1 ) × ( 0 , ) and h ( 0 , 1 ) × [ 0 , ) [ 0 , ) are continuous. So our nonlinearity may be singular at t = 0 , 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.

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