Existence Theory

1977 ◽  
pp. 268-312
Author(s):  
R. D. Driver
Keyword(s):  
Existence Theory

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

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

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