TY - JOUR
A2 - Infante, Gennaro
AU - Wang, Jinxiang
AU - Ma, Ruyun
AU - Wen, Jin
PY - 2017
DA - 2017/07/24
TI - *S*-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation
SP - 1069491
VL - 2017
AB - We investigate the existence of S-shaped connected component in the set of positive solutions of the fourth-order boundary value problem: u′′′′x=λhxfux, x∈(0,1),u(0)=u(1)=u′′0=u′′1=0, where λ>0 is a parameter, h∈C[0,1], and f∈C[0,∞) with f0≔lims→0(f(s)/s)=∞. We develop a bifurcation approach to deal with this extreme situation by constructing a sequence of functions f[n] satisfying f[n]→f and (f[n])0→∞. By studying the auxiliary problems, we get a sequence of unbounded connected components C[n], and, then, we find an unbounded connected component C in the set of positive solutions of the fourth-order boundary value problem which satisfies 0,0∈C⊂limsupC[n] and is S-shaped.
SN - 2314-8896
UR - https://doi.org/10.1155/2017/1069491
DO - 10.1155/2017/1069491
JF - Journal of Function Spaces
PB - Hindawi
KW -
ER -