MathDB

Finiteness conjecture for smooth global solutions

Consider the differential equation

anditssmoothglobalsolutions.∗∗Finitenessconjecture.∗∗Thereareonlyfinitelymanysmoothglobalsolutionstoand its smooth global solutions. **Finiteness conjecture.** There are only finitely many smooth global solutions to

. This finiteness would justify the use of a numerical solver to determine the number of global solutions for a given M-shaped ϕ\phi, and the source leaves it as an open conjecture.

Sources & referencesView supporting material

Primary source

Michael Robinson, “Eternal solutions and heteroclinic orbits of a semilinear parabolic equation”, arXiv:0804.4883 (2008).

dynamical-systemsordinary-differential-equations

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.