Multiple positive solutions to third-order three-point singular semipositone boundary value problem

Details Multiple positive solutions to third-order three-point singular semipositone boundary value problem Multiple positive solutions to third-order three-point singular semipositone boundary value problem

2005-03-05

arxiv.org/abs/math/0503094v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 409-422

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: $\begin{cases} x'''(t)-\ld f(t,x) =0, &t\in(0,1); [.3pc] x(0)=x'(\eta)=x''(1)=0, & \end{cases}$ where ${1/2}<\eta<1$, the non-linear term $f(t,x):(0,1)\times(0,+\i)\to (-\i,+\i)$ is continuous and may be singular at $t=0$, $t=1$, and $x=0$, also may be negative for some values of $t$ and $x$, $\ld$ is a positive parameter.

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