EXISTENCE RESULTS FOR FIXED AND FREE DISCONTINUITIES PROBLEMS WITH DEVIATING ARGUMENTS

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.

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

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-014-0219-8 ◽

2014 ◽

Vol 17 (4) ◽

Cited By ~ 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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New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

Boundary Value Problems ◽

10.1186/s13661-021-01512-x ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Osama Moaaz ◽

Choonkil Park ◽

Elmetwally M. Elabbasy ◽

Waed Muhsin

Keyword(s):

Differential Equations ◽

Second Order ◽

The Other ◽

Riccati Transformation ◽

Transformation Technique ◽

Deviating Arguments ◽

Neutral Differential Equations ◽

Second Order Differential Equations ◽

Continuous Delay ◽

New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

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Ordinary Differential Equations with Nonlinear Boundary Conditions

Georgian Mathematical Journal ◽

10.1515/gmj.2002.287 ◽

2002 ◽

Vol 9 (2) ◽

pp. 287-294

Author(s):

Tadeusz Jankowski

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Ordinary Differential Equations ◽

Nonlinear Boundary ◽

Nonlinear Boundary Conditions ◽

Existence Results ◽

Monotone Iterative Technique ◽

Lower And Upper Solutions ◽

Iterative Technique ◽

Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

Nonautonomous Dynamical Systems ◽

10.1515/msds-2020-0121 ◽

2020 ◽

Vol 7 (1) ◽

pp. 272-280

Author(s):

Mamadou Abdoul Diop ◽

Kora Hafiz Bete ◽

Reine Kakpo ◽

Carlos Ogouyandjou

Keyword(s):

Differential Equations ◽

Resolvent Operator ◽

Mild Solutions ◽

Linear Part ◽

Nonlocal Conditions ◽

Existence Results ◽

Fréchet Spaces ◽

Local Conditions ◽

State Dependent ◽

Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

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A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

Advances in Difference Equations ◽

10.1186/s13662-021-03502-w ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Ahmed Nouara ◽

Abdelkader Amara ◽

Eva Kaslik ◽

Sina Etemad ◽

Shahram Rezapour ◽

...

Keyword(s):

Stability Analysis ◽

Boundary Value Problem ◽

Fractional Derivatives ◽

Boundary Value ◽

Research Work ◽

Existence Results ◽

Fractional Boundary Value Problem ◽

Numerical Examples ◽

Fractional Derivatives And Integrals ◽

Fractional Differential

AbstractIn this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

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