A fully nonlinear characteristic method for gyrokinetic simulation

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

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Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

Advances in Difference Equations ◽

10.1186/s13662-020-03039-4 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Liyun Jin ◽

Hua Luo

Keyword(s):

Positive Solutions ◽

Fixed Point Index ◽

Nonlinear Term ◽

Boundary Value ◽

Index Theory ◽

Second Order ◽

Fully Nonlinear ◽

Fixed Point Index Theory ◽

Weaker Conditions ◽

Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

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Existence of Solutions with Asymptotic Behavior of Exterior Problems of Fully Nonlinear Uniformly Elliptic Equations

2011 Fourth International Symposium on Knowledge Acquisition and Modeling ◽

10.1109/kam.2011.63 ◽

2011 ◽

Author(s):

Limei Da

Keyword(s):

Asymptotic Behavior ◽

Elliptic Equations ◽

Existence Of Solutions ◽

Fully Nonlinear ◽

Exterior Problems

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Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0009 ◽

2020 ◽

Vol 21 (1) ◽

pp. 11-21

Author(s):

Lin Zhao ◽

Weihao Meng ◽

Zhongqiang Zheng ◽

Zongyu Chang

Keyword(s):

Nonlinear Dynamics ◽

Dynamic Behavior ◽

Coupling Factor ◽

Dynamic Responses ◽

Mooring Line ◽

Second Law ◽

Largest Lyapunov Exponent ◽

Nonlinear Characteristic ◽

Runge Kutta Method ◽

Marine Engineering

AbstractTethered submerged buoy is used extensively in the field of marine engineering. In this paper considering the effect of wave, the nonlinear dynamics behavior of tethered submerged buoy is debated under wave loadings. According to Newton’s second law, the dynamic of the system is built. The coupling factor of the system is neglected, the natural frequency is calculated. The dynamic responses of the system are analyzed using Runge–Kutta method. Considering the variety of the steepness kA, the phenomenon of dynamic behavior can be periodic, double periodic and quasi-periodic and so on. The bifurcation diagram and the largest Lyapunov exponent are applied to judge the nonlinear characteristic. It is helpful to understand the dynamic behavior of tethered submerged buoy and design the mooring line of tethered submerge buoy.

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