Degree, instability and bifurcation of reaction–diffusion systems with obstacles near certain hyperbolas

Critical points for reaction-diffusion system with one and two unilateral conditions

“…Numerically it seems that the nodal properties of v are preserved along a large part of the right-most branches (going to the right which seems to be bounded in d 2 ) of K D , K x1 as well as of K x1 . This boundedness perfectly fits with the theoretical results for BVPs with unilateral conditions prescribed on the boundary, see [1,2,4]. As far as (more precisely, as close as to the origin) we can go with d = (d 1 , d 2 ) along the right-most branches while the profile of v satisfies simultaneously sharp inequality in (2.8) and v( ) ≥ 0, such d belongs also to U x1 .…”