TY - JOUR
T1 - On the neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type
AU - Ni, Wei Ming
AU - Takagi, Izumi
PY - 1986/9
Y1 - 1986/9
N2 - We derive a priori estimates for positive solutions of the Neumann problem for some semilinear elliptic systems (i.e., activator-inhibitor systems in biological pattern formation theory), as well as for semilinear single equations related to such systems. By making use of these a priori estimates, we show that under certain assumptions, there is no positive nonconstant solutions for single equations or for activator-inhibitor systems when the diffusion coefficient (of the activator, in the case of systems) is sufficiently large; we also study the existence of nonconstant solutions for specific domains.
AB - We derive a priori estimates for positive solutions of the Neumann problem for some semilinear elliptic systems (i.e., activator-inhibitor systems in biological pattern formation theory), as well as for semilinear single equations related to such systems. By making use of these a priori estimates, we show that under certain assumptions, there is no positive nonconstant solutions for single equations or for activator-inhibitor systems when the diffusion coefficient (of the activator, in the case of systems) is sufficiently large; we also study the existence of nonconstant solutions for specific domains.
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U2 - 10.1090/S0002-9947-1986-0849484-2
DO - 10.1090/S0002-9947-1986-0849484-2
M3 - Article
AN - SCOPUS:0001548639
SN - 0002-9947
VL - 297
SP - 351
EP - 368
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 1
ER -