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

VL - 297

SP - 351

EP - 368

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -