scholarly journals Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

2021 ◽  
Vol 26 (2) ◽  
pp. 315-333
Author(s):  
Xinguang Zhang ◽  
Lishan Liu ◽  
Yonghong Wu ◽  
B. Wiwatanapataphee ◽  
Yujun Cui
Keyword(s):  
Positive Solutions ◽  
Exterior Domain ◽  
Schrodinger Equation ◽  
Existence Theorems ◽  
Asymptotic Properties ◽  
Fluid Flows ◽  
Analytical Techniques ◽  
Space Theory ◽  
Nonlinear Elliptic ◽  
Special Cases

In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows.

POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 823-837 ◽  
Author(s):  
A. CAÑADA ◽  
J.L. GÁMEZ
Keyword(s):  
Positive Solutions ◽  
Nonlinear Interaction ◽  
Spatial Dependence ◽  
Global Bifurcation ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Systems ◽  
Decoupling Method ◽  
Nonlinear Elliptic ◽  
Cooperative Models

In this paper we prove the existence of nonnegative and non-trivial solutions of problems of the form [Formula: see text] Our main result improves many previous results of other authors and it may be applied to study the three standard situations: competition, prey-predator and cooperative models. We also cover some other cases which, due essentially to the spatial dependence or to a nonlinear interaction, are not any of these three types. The method of proof combines a decoupling method with a global bifurcation result.

EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS

2004 ◽  
Vol 02 (01) ◽  
pp. 71-85 ◽  
Author(s):  
YUJI LIU ◽  
WEIGAO GE
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Order Ordinary Differential Equation ◽  
Order Four

In this paper, we study four-point boundary value problems for a fourth-order ordinary differential equation of the form [Formula: see text] with one of the following boundary conditions: [Formula: see text] or [Formula: see text] Growth conditions on f which guarantee existence of at least three positive solutions for the problems (E)–(B1) and (E)–(B2) are imposed.

Analytical Techniques for the Optimisation of Rocket Trajectories

1963 ◽  
Vol 14 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Derek F. Lawden
Keyword(s):  
Gravitational Field ◽  
Artificial Satellite ◽  
Analytical Techniques ◽  
Present Position ◽  
Mayer Problem ◽  
Special Cases ◽  
Minimum Expenditure ◽  
Law Of Attraction ◽  
Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

scholarly journals Some asymptotic properties of SEIRS models with nonlinear incidence and random delays

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Divine Wanduku ◽  
B.O. Oluyede
Keyword(s):  
Differential Equations ◽  
Incidence Rate ◽  
Delay Differential Equations ◽  
Vivax Malaria ◽  
Asymptotic Properties ◽  
Analytical Techniques ◽  
Distributed Delays ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Delay Differential

This paper presents the dynamics of mosquitoes and humans with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN  R0* and  ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given.

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