abstract equation
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1989 ◽  
Vol 112 (1-2) ◽  
pp. 135-143 ◽  
Author(s):  
J. Esquinas ◽  
J. López-Gómez

SynopsisIn some cases, a reaction–diffusion system can be transformed into an abstract equation where the linear part is given by a polynomial of a linear operator, say Multiparameter bifurcation for this equation is considered as the coefficients of the operator polynomial in are varied.


ChemInform ◽  
1988 ◽  
Vol 19 (36) ◽  
Author(s):  
KH. I. AMIRKHANOV ◽  
I. M. ABDULAGATOV ◽  
B. G. ALIBEKOV ◽  
G. V. STEPANOV ◽  
O. A. BOUY

1987 ◽  
Vol 36 (1) ◽  
pp. 25-37 ◽  
Author(s):  
J. Esquinas ◽  
J. López-Gómez

Let us consider the abstract equation(0.1) L (ɛ) u + F (ɛ,u) = 0,where F (ɛ,u) = 0 (|u|2) for ɛ near zero. In this paper we define a multiplicity depending only on L (ɛ) allowing us to obtain the following result: “Odd multiplicity entails bifurcation and, if the multiplicity is even, it is possible to find F (ɛ,u) such that the only solution to (0.1) near the origin are the trivial ones”.


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