Global bifurcation for fill's equation with nonlinear boundary conditions

1994 ◽  
Vol 55 (1-2) ◽  
pp. 7-24
Author(s):  
Mrziglod Thomas
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Nonlinear Boundary Conditions

scholarly journals Continuum of one-sign solutions of one-dimensional Minkowski-curvature problem with nonlinear boundary conditions

2021 ◽  
Author(s):  
Yanqiong Lu ◽  
Zhengqi Jing
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Nonlinear Boundary Conditions ◽  
Continuous Functions ◽  
One Dimensional ◽  
Curvature Equation ◽  
Existence And Multiplicity ◽  
Curvature Problem ◽  
The Continuum

In this work, we investigate the continuum of one-sign solutions of the nonlinear one-dimensional Minkowski-curvature equation $$-\big(u’/\sqrt{1-\kappa u’^2}\big)’=\lambda f(t,u),\ \ t\in(0,1)$$ with nonlinear boundary conditions $u(0)=\lambda g_1(u(0)), u(1)=\lambda g_2(u(1))$ by using unilateral global bifurcation techniques, where $\kappa>0$ is a constant, $\lambda>0$ is a parameter $g_1,g_2:[0,\infty)\to (0,\infty)$ are continuous functions and $f:[0,1]\times[-\frac{1}{\sqrt{\kappa}},\frac{1}{\sqrt{\kappa}}]\to\mathbb{R}$ is a continuous function. We prove the existence and multiplicity of one-sign solutions according to different asymptotic behaviors of nonlinearity near zero.

Global bifurcation for a special Hill equation with nonlinear boundary conditions

1992 ◽  
Vol 43 (2) ◽  
pp. 328-334 ◽  
Author(s):  
Norman W. Bazley ◽  
Thomas Mrziglod
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Nonlinear Boundary Conditions ◽  
Hill Equation

Ordinary Differential Equations with Nonlinear Boundary Conditions

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.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

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