Optimal results in local bifurcation theory
1987 ◽
Vol 36
(1)
◽
pp. 25-37
◽
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”.
1989 ◽
Vol 49
(1)
◽
pp. 72-85
◽
Keyword(s):
1988 ◽
pp. 222-341
2018 ◽
Vol 474
(2216)
◽
pp. 20180038
2002 ◽
Vol 48
(8)
◽
pp. 1077-1086
◽
1988 ◽
Vol 75
(2)
◽
pp. 206-215
◽
1977 ◽
1988 ◽
Vol 71
(1)
◽
pp. 72-92
◽