Titlebook: Critical Point Theory; Sandwich and Linking Martin Schechter Book 2020 The Editor(s) (if applicable) and The Author(s), under exclusive lic

较早

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

antiandrogen

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

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

Synchronism

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

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

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

GLUT