Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 03, pp 1-11.
Title: Positive solutions and nonlinear multipoint conjugate
eigenvalue problems
Authors: Paul W. Eloe (Univ. of Dayton, USA}
Johnny Henderson (Auburn Univ., USA)
Abstract:
Values of $\lambda$ are determined for which there exist solutions in a
cone of the $n^{th}$ order nonlinear differential equation,
$$u^{(n)} = \lambda a(t) f(u)\,,\quad 0 < t < 1\,,$$
satisfying the multipoint boundary conditions,
$$u^{(j)}(a_i) = 0\,,\quad 0\leq j\leq n_i -1\,,\quad 1 \leq i \leq k\,,$$
where $0 = a_1 < a_2 < \cdots < a_k = 1$, and $\sum _{i=1}^k n_i = n$,
where $a$ and $f$ are nonnegative valued, and where both
$\lim\limits_{|x| \to 0^+} f(x)/|x|$ and
$\lim\limits_{|x| \to\infty} f(x)/|x|$ exist.
Submitted December 17, 1996. Published January 22, 1997.
Math Subject Classification: 34B10, 34B15.
Key Words: multipoint; nonlinear eigenvalue problem; cone.