Bifurcation near degenerate families

Abstract

Suppose x,A,Zare Banach space, is a smooth function and the equation

for λ=0, has a one parameter family of smooth solutions p(s), 0≤s,≤1, p(0)=p(1) with the objective is to discuss the solutions of (1) near Γ for λ in a neighborhood of zero. Asuming is Fredholm of index zero and the authors have previously given a solution to this problem under natural hypotheses on M.In this paper, the case where is considered. Applications are given to the effect of small damping and small forcing on the existence of periodic solutions near a periodic solution of an autonomous Hamiltonian system

^†This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3092, the U.S. Army Research Office under AROD AAG 29-76-G-0294, National science Foundation, under MCS 76-07247

^‡This research was supported in part by FAPESP (Fundäo de Amparo á Pesquisa do Estado de Säo Paulo) under proc. 75/1227

^†This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3092, the U.S. Army Research Office under AROD AAG 29-76-G-0294, National science Foundation, under MCS 76-07247

^‡This research was supported in part by FAPESP (Fundäo de Amparo á Pesquisa do Estado de Säo Paulo) under proc. 75/1227

Notes

^†This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3092, the U.S. Army Research Office under AROD AAG 29-76-G-0294, National science Foundation, under MCS 76-07247

^‡This research was supported in part by FAPESP (Fundäo de Amparo á Pesquisa do Estado de Säo Paulo) under proc. 75/1227