TY - JOUR
T1 - Bifurcation from zero or infinity in Sturm-Liouville problems which are not linearizable
AU - Rynne, Bryan Patrick
PY - 1998/12
Y1 - 1998/12
N2 - We consider the nonlinear Sturm-Liouville problem[formula][formula]whereai,biare real numbers with ai+bi0,i=0,1, ? is a real parameter, and the functionspandaare strictly positive on [0,p]. Suppose that the nonlinearityhsatisfies a condition of the form[formula]as either (?,?)?0 or (?,?)?8, for some constantsM0,M1. Then we show that there exist global continua of nontrivial solutions (?,u) bifurcating fromu=0 or "u=8," respectively. These global continua have properties similar to those of the continua found in Rabonowitz' well-known global bifurcation theorem. © 1998 Academic Press.
AB - We consider the nonlinear Sturm-Liouville problem[formula][formula]whereai,biare real numbers with ai+bi0,i=0,1, ? is a real parameter, and the functionspandaare strictly positive on [0,p]. Suppose that the nonlinearityhsatisfies a condition of the form[formula]as either (?,?)?0 or (?,?)?8, for some constantsM0,M1. Then we show that there exist global continua of nontrivial solutions (?,u) bifurcating fromu=0 or "u=8," respectively. These global continua have properties similar to those of the continua found in Rabonowitz' well-known global bifurcation theorem. © 1998 Academic Press.
UR - http://www.scopus.com/inward/record.url?scp=0002518904&partnerID=8YFLogxK
U2 - 10.1006/jmaa.1998.6122
DO - 10.1006/jmaa.1998.6122
M3 - Article
SN - 0022-247X
VL - 228
SP - 141
EP - 156
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -