Steady-state bifurcation of a nonlinear boundary problem

2022 ◽  
pp. 107902
Author(s):  
Dan Wei ◽  
Shangjiang Guo
Keyword(s):  
Steady State ◽  
Boundary Problem ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Problem ◽  
Steady State Bifurcation

Green’s functions, positive solutions, and a Lyapunov inequality for a caputo fractional-derivative boundary value problem

2019 ◽  
Vol 22 (3) ◽  
pp. 750-766 ◽  
Author(s):  
Xiangyun Meng ◽  
Martin Stynes
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Problem ◽  
Caputo Fractional Derivative ◽  
Caputo Derivative ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Lyapunov Inequality ◽  
Nonlinear Boundary Problem

Abstract We consider a nonlinear boundary problem whose highest-order derivative is a Caputo derivative of order α with 1 < α < 2. Properties of its associated Green’s function are derived. These properties enable us to deduce sufficient conditions for the existence of a positive solution to the boundary value problem and to prove a Lyapunov inequality for the problem. Our results sharpen and extend earlier results of other authors.

Current-Phase Relation in Josephson Junctions with Complex Ferromagnetic/Normal Metal Interlayers

2012 ◽  
Vol 190 ◽  
pp. 401-404 ◽  
Author(s):  
S. V. Bakurskiy ◽  
N. V. Klenov ◽  
T. Yu. Karminskaya ◽  
M. Yu. Kupriyanov ◽  
V. K. Kornev
Keyword(s):  
Boundary Problem ◽  
Phase Relation ◽  
Josephson Junctions ◽  
Nonlinear Boundary ◽  
Phase Relations ◽  
Normal Metal ◽  
Current Phase ◽  
Two Dimensional ◽  
Nonlinear Boundary Problem ◽  
Usadel Equation

In the frame of Usadel equation the two-dimensional nonlinear boundary problem for heterostructures with complex ferromagnetic (F)/normal metal (N) interlayer has been solved numerically for arbitrary values of electrodes spacing L, thickness dN and dF of N and F films. We calculate the current-phase relations for ramp-type S-NF-S and overlap-type SFN-FN-NFS junctions. We have found the range of parameters providing an opportunity for realization of Josephson φ-junction based on the considered structures.

Freeform illumination design: a nonlinear boundary problem for the elliptic Monge–Ampére equation

2013 ◽  
Vol 38 (2) ◽  
pp. 229 ◽  
Author(s):  
Rengmao Wu ◽  
Liang Xu ◽  
Peng Liu ◽  
Yaqin Zhang ◽  
Zhenrong Zheng ◽  
...  
Keyword(s):  
Boundary Problem ◽  
Nonlinear Boundary ◽  
Illumination Design ◽  
Nonlinear Boundary Problem ◽  
Monge Ampere

scholarly journals A nonlinear boundary problem involving thep-bilaplacian operator

2005 ◽  
Vol 2005 (10) ◽  
pp. 1525-1537 ◽  
Author(s):  
Abdelouahed El Khalil ◽  
Siham Kellati ◽  
Abdelfattah Touzani
Keyword(s):  
Boundary Conditions ◽  
Boundary Problem ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Nondecreasing Sequence ◽  
Nonlinear Boundary Problem

We show some new Sobolev's trace embedding that we apply to prove that the fourth-order nonlinear boundary conditionsΔp2u+|u|p−2u=0inΩand−(∂/∂n)(|Δu|p−2Δu)=λρ|u|p−2uon∂Ωpossess at least one nondecreasing sequence of positive eigenvalues.

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