Existence Theory of NFDE with Infinite Delay

1994 ◽  
pp. 47-73
Author(s):  
V. Lakshmikantham ◽  
Lizhi Wen ◽  
Binggen Zhang
Keyword(s):  
Infinite Delay ◽  
Existence Theory

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

scholarly journals Asymptotically ordinary linear Volterra difference equations with infinite delay

2020 ◽  
Vol 386 ◽  
pp. 125499
Author(s):  
Áron Fehér ◽  
Lőrinc Márton ◽  
Mihály Pituk
Keyword(s):  
Difference Equations ◽  
Infinite Delay ◽  
Volterra Difference Equations

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.

scholarly journals An Existence Theory for Gravity–Capillary Solitary Water Waves

Water Waves ◽  
2021 ◽  
Author(s):  
M. D. Groves
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Applied Mathematics ◽  
Spatial Dynamics ◽  
Existence Theory ◽  
Water Wave Problem ◽  
Reduction Methods ◽  
Centre Manifold Reduction ◽  
Weak Surface ◽  
The One

AbstractIn the applied mathematics literature solitary gravity–capillary water waves are modelled by approximating the standard governing equations for water waves by a Korteweg-de Vries equation (for strong surface tension) or a nonlinear Schrödinger equation (for weak surface tension). These formal arguments have been justified by sophisticated techniques such as spatial dynamics and centre-manifold reduction methods on the one hand and variational methods on the other. This article presents a complete, self-contained account of an alternative, simpler approach in which one works directly with the Zakharov–Craig–Sulem formulation of the water-wave problem and uses only rudimentary fixed-point arguments and Fourier analysis.

scholarly journals Existence theory: Outline for a theory of social behaviour

2021 ◽  
pp. 1468795X2199824
Author(s):  
Patrick Baert ◽  
Marcus Morgan ◽  
Rin Ushiyama
Keyword(s):  
Formal Education ◽  
Sociological Theory ◽  
Forced Migration ◽  
Existence Theory ◽  
Power Dynamics ◽  
Structural Factors ◽  
Contemporary Society ◽  
Social Phenomena ◽  
New Approach ◽  
Cultural Expectations

This article introduces ‘existence theory’ as a new approach to sociological theory and research. Existence theory starts from the assumption that people organise their lives around a limited set of existential milestones. Cultural expectations are such that without the accomplishment of those milestones, individuals may experience their lives as incomplete. Examples of milestones can include the attainment of formal education, a lasting partnership and the creation of a family, but in general the milestones which are important to individuals and their precise articulation will depend on a variety of cultural and structural factors. The achievement of existential milestones often depends on that of other existential milestones, thereby producing what we call an ‘existential ladder’. The article also elaborates on the significance of ‘existential urgency’ in that, due to a variety of factors (some biological, some cultural and structural), there are time limits on when certain existential milestones ought to be achieved by. In contemporary society, we note that individuals seem to have more choice about which milestones are important to them and when they can be achieved, although we emphasise that this flexibility is unevenly distributed. This then provides a steppingstone towards an elaboration of the power dynamics and inequalities underlying both the experience and the achievement of existential milestones. Finally, this paper shows how existence theory helps to reflect on a variety of social phenomena of contemporary significance: populism in politics, forced migration, and the coronavirus pandemic.

scholarly journals Stability analysis of solutions and existence theory of fractional Lagevin equation

2021 ◽  
Vol 60 (4) ◽  
pp. 3641-3647
Author(s):  
Amita Devi ◽  
Anoop Kumar ◽  
Thabet Abdeljawad ◽  
Aziz Khan
Keyword(s):  
Stability Analysis ◽  
Existence Theory

scholarly journals Shadowing for nonautonomous difference equations with infinite delay

2021 ◽  
pp. 107284
Author(s):  
Davor Dragičević ◽  
Mihály Pituk
Keyword(s):  
Difference Equations ◽  
Infinite Delay
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