Some existence results for a stochastic differential system with non-Lipschitz conditions

Stochastics ◽  
2021 ◽  
pp. 1-14
Author(s):  
Vikram Singh
Keyword(s):  
Differential System ◽  
Existence Results ◽  
Lipschitz Conditions

On the existence of mild solutions for a class of fractional differential equations with nonlocal conditions in the α-norm

2014 ◽  
Vol 51 (2) ◽  
pp. 141-154
Author(s):  
Mohamed Abbas
Keyword(s):  
Cauchy Problem ◽  
Mild Solutions ◽  
Linear Part ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Existence Results ◽  
Nonlinear Part ◽  
Fractional Differential ◽  
Fractional Cauchy Problem ◽  
Lipschitz Conditions

This paper concerns the existence of mild solutions for some fractional Cauchy problem with nonlocal conditions in the α-norm. The linear part of the equations is assumed to generate an analytic compact bounded semigroup, and the nonlinear part satisfies some Lipschitz conditions with respect to the fractional power norm of the linear part. By using a fixed point theorem of Sadovskii, we establish some existence results which generalize ones in the case of fractional order derivative.

scholarly journals Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Douglas R. Anderson ◽  
Christopher C. Tisdell
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
A Priori ◽  
Sufficient Conditions ◽  
Linear Interpolation ◽  
Existence Results ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Continuous Boundary ◽  
Lipschitz Conditions

We investigate two types of first-order, two-point boundary value problems (BVPs). Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP). We formulate some sufficient conditions under which the discrete BVP will admit solutions. For this, our choice of methods involves a monotone iterative technique and the method of successive approximations (a.k.a. Picard iterations) in the absence of Lipschitz conditions. Our existence results for the discrete BVP are of a constructive nature and are of independent interest in their own right. We then turn our attention to applying our existence results for the discrete BVP to the continuous BVP. We form new existence results for solutions to the continuous BVP with our methods involving linear interpolation of the data from the discrete BVP, combined witha prioribounds and the convergence Arzela-Ascoli theorem. Thus, our use of discrete BVPs to yield results for the continuous BVP may be considered as a discrete approach to continuous BVPs.

scholarly journals Positive solutions to n-dimensional $\alpha _{1}+\alpha _{2}$ order fractional differential system with p-Laplace operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tian Wang ◽  
Guo Chen ◽  
Huihui Pang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

AbstractIn this paper, we study an n-dimensional fractional differential system with p-Laplace operator, which involves multi-strip integral boundary conditions. By using the Leggett–Williams fixed point theorem, the existence results of at least three positive solutions are established. Besides, we also get the nonexistence results of positive solutions. Finally, two examples are presented to validate the main results.

scholarly journals New existence results for coupled delayed differential systems with multi-parameters

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ruipeng Chen ◽  
Xiaoya Li
Keyword(s):  
Fixed Point ◽  
Differential System ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Differential Systems ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Functional Differential ◽  
Functional Differential System

AbstractIn this paper, several novel existence and multiplicity results are established for a coupled functional differential system with multi-parameters. The discussion is based upon fixed point theory, and our main findings enrich and complement those available in the literature.

scholarly journals Multiple Positive Periodic Solutions for Delay Differential System

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Zhao-Cai Hao ◽  
Ti-Jun Xiao ◽  
Jin Liang
Keyword(s):  
Positive Integer ◽  
Periodic Solutions ◽  
Differential System ◽  
Existence Results ◽  
Positive Periodic Solutions ◽  
Differential Systems ◽  
Delay Differential System ◽  
Delay Differential Systems ◽  
Delay Differential

We obtain some existence results for multiple positive periodic solutions of some delay differential systems. Examples are presented as applications. For a general positive integerm≥2, main results of this paper do not appear in former literatures as we know. Comparing with the existing results, our results are new also whenm=1.

scholarly journals Existence of Gibbs point processes with stable infinite range interaction

2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur
Keyword(s):  
Point Processes ◽  
Existence Results ◽  
Pairwise Interaction ◽  
Range Interaction ◽  
Pairwise Interactions ◽  
Gibbs Point Processes ◽  
Infinite Range Interactions ◽  
Finite Configuration ◽  
Multi Body ◽  
Infinite Range

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

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