EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS

• Published in: Proceedings of the Edinburgh Mathematical Society Vol. 46; no. 2; pp. 279 - 292
• Main Author: Ma, Ruyun
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.06.2003
• Subjects: Boundary value problems; cones; fixed-point theorem; multipoint boundary-value problems; positive solutions; positive solutions; fixed-point theorem; multipoint boundary-value problems; cones
• ISSN: 0013-0915; 1464-3839
• DOI: 10.1017/S0013091502000391

In this paper we consider the existence of positive solutions to the boundary-value problems \begin{align*} (p(t)u')'-q(t)u+\lambda f(t,u)\amp=0,\quad r\ltt\ltR, \\[2pt] au(r)-bp(r)u'(r)\amp=\sum^{m-2}_{i=1}\alpha_iu(\xi_i), \\ cu(R)+dp(R)u'(R)\amp=\sum^{m-2}_{i=1}\beta_iu(\xi_i), \end{align*} where $\lambda$ is a positive parameter, $a,b,c,d\in[0,\infty)$, $\xi_i\in(r,R)$, $\alpha_i,\beta_i\in[0,\infty)$ (for $i\in\{1,\dots m-2\}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones. AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15