Electron. J. Diff. Eqns., Vol. 1997(1997), No. 03, pp 1-11.

Positive solutions and nonlinear multipoint conjugate eigenvalue problems

Paul W. Eloe & Johnny Henderson

Abstract:
Values of $\lambda$ are determined for which there exist solutions in a cone of the $n^{th}$ order nonlinear differential equation,
$u^{(n)} = \lambda a(t) f(u)$ 0 less than $t$ less than 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 $0 = a_1$ less than $a_2$ less than ... less than $a_k = 1$, 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.

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Paul W. Eloe
Department of Mathematics, University of Dayton, Dayton, Ohio 45469-2316 USA
e-mail: Paul.Eloe@notes.udayton.edu

Johnny Henderson
department of Mathematics, Auburn University, Auburn, AL 36849 USA
e-mail: hendej2@mail.auburn.edu

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