Abstract
We consider the nonlinear eigenvalue problems
u″+rf(u)=0,
0<t<1,
u(0)=0,
u(1)=∑i=1m−2αiu(ηi),
where
m≥3,
ηi∈(0,1),
and
αi>0
for
i=1,…,m−2,
with
∑i=1m−2αi<1;
r∈ℝ;
f∈C1(ℝ,ℝ).
There exist two constants
s2<0<s1
such that
f(s1)=f(s2)=f(0)=0
and
f0:=limu→0(f(u)/u)∈(0,∞),
f∞:=lim|u|→∞(f(u)/u)∈(0,∞).
Using the global bifurcation techniques, we study the global
behavior of the components of nodal solutions of the above
problems.