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the systems of nonlinear equations of gierer - meinhardt type have received a considerable attention in the last decade .
these problems arise in the study of biological pattern formation by auto and cross catalysis being related to known biochemical processes and cellular properties . the general model proposed by gierer and meinhardt @xcite
may be written as \ {       .
@xmath0 by the maximum principle , it follows that @xmath1 in @xmath2 , i.e. , @xmath3 in @xmath2 .
this yields @xmath4 in @xmath2 which again contradicts proposition [ psign ] .
the proof of ( iv ) follows in the same manner .       of the system @xmath5 with @xmath6 , @xmath7 , @xmath8 , @xmath9 and @xmath10 .
we have chosen @xmath11 ( on the left ) and @xmath12 ( on the right).,title="fig:",height=226 ]   of the system @xmath5 with @xmath6 , @xmath7 , @xmath8 , @xmath9 and @xmath10 .
we have chosen @xmath11 ( on the left ) and @xmath12 ( on the right).,title="fig:",height=226 ]      * remark . * as a consequence of theorem [ texi ] , the solution @xmath13 of the system can be approximated by the solutions of @xmath14 .
furthermore , the shooting method combined with the broyden method in order to avoid the derivatives , are suitable to numerically approximate the solution of . we have considered @xmath6 , @xmath7 , @xmath8 , @xmath9 and @xmath15 . in the above figure we have plotted the solution @xmath13 of @xmath5 for @xmath11 ( on the left ) and @xmath12 ( on the right ) respectively .
we study the existence and nonexistence of classical solutions to a general gierer - meinhardt system with dirichlet boundary condition . 
 the main feature of this paper is that we are concerned with a model in which both the activator and the inhibitor have different sources given by general nonlinearities . under some additional hypotheses and in case of pure powers in nonlinearities , regularity and uniqueness of the solution in one dimension is also presented . 
 + * 2000 mathematics subject classification * : 35j55 , 35j65 . + * key words * : gierer - meinhardt ; elliptic system ; activator - inhibitor ; maximum principle .     
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