Existence and uniqueness theorems for a third-order generalized boundary value problem
1989 ◽
Vol 2
(1)
◽
pp. 33-51
Keyword(s):
Let f:[0,1]×ℝ3→ℝ be a function satisfying Caratheodory's conditions, e(x)∈L1[0,1], η∈[0,1], h≥0, k≥0, h+k>0. This paper studies existence and uniqueness questions for the third-order three-point generalized boundary value problem u‴+f(x,u,u′,u″)=e(x), 0<x<1, u(η)=0, u″(0)−hu′(0)=u″(1)+ku′(1)=0, and the associated special cases corresponding to one or both of h and k equal to infinity. The conditions on the nonlinearity f turn out to be related to the spectrum of the linear boundary value problem u‴=λu′, u(η)=0, u″(0)−hu′(0)=u″(1)+ku′(1)=0, in a natural way.
1962 ◽
Vol 103
(3)
◽
pp. 559
1961 ◽
Vol 101
(2)
◽
pp. 351-351
1991 ◽
Vol 16
(11)
◽
pp. 949-957
◽
2012 ◽
Vol 3
(3)
◽
pp. 194-200
Keyword(s):
1975 ◽
Vol 2
(3)
◽
pp. 241-249
◽
Keyword(s):