较早
发表于 2025-3-23 11:49:00
Nonlinear Optics,Steady state solutions satisfy the following equation over a periodic domain . . where ., . are parameters. The solutions . are to be periodic in Ω with the same periods as those of Ω. This equation has the trivial solution . = 0.
暴露他抗议
发表于 2025-3-23 16:52:20
http://reply.papertrans.cn/25/2401/240087/240087_12.png
antiandrogen
发表于 2025-3-23 18:27:31
ce. This is just what is needed. For such applications it would be very helpful if we could obtain a bounded sequence satisfying (4.1). This leads to the question: Is there anything we can do to obtain such a sequence?
单独
发表于 2025-3-23 23:14:11
The Monotonicity Trick,ce. This is just what is needed. For such applications it would be very helpful if we could obtain a bounded sequence satisfying (4.1). This leads to the question: Is there anything we can do to obtain such a sequence?
饮料
发表于 2025-3-24 03:10:05
http://reply.papertrans.cn/25/2401/240087/240087_15.png
Synchronism
发表于 2025-3-24 06:39:19
Linking Systems,s the required extremum.This worked fairly well in one dimension where .(.) = 0 is an ordinary differential equation. However, in higher dimensions, it turned out that it was easier to find the extrema of . than solve .(.) = 0. This led to the approach of solving equations of the form .(.) = 0 by finding extrema of ..
故意
发表于 2025-3-24 14:14:21
Linking Systems, a .. functional(usually representing the energy) arising from the given data. As an illustration, the equation . is the Euler equation of the functional . on an appropriate space, where . and the norm is that of ... The solving of the Euler equations is tantamount to finding critical points of the
deriver
发表于 2025-3-24 17:50:38
Sandwich Systems,ir does not separate the functional, nothing can be said concerning a potential critical point. This raises the questions, “Is there anything one can do if one cannot find linking sets that separate the functional?” “Are there sets that can lead to critical sequences even though they do not separate
TAIN
发表于 2025-3-24 21:05:24
http://reply.papertrans.cn/25/2401/240087/240087_19.png
GLUT
发表于 2025-3-24 23:21:39
http://reply.papertrans.cn/25/2401/240087/240087_20.png