# POSITIVE SOLUTIONS IN AN ANNULUS FOR NONLINEAR DIFFERENTIAL EQUATIONS ON A MEASURE CHAIN

## DOI:

https://doi.org/10.5556/j.tkjm.30.1999.4230## Keywords:

Differential equation, measure chain, boundary value problem## Abstract

We study the existence of positive solutions of the second order differential equation in an annulus on a measure chain, $u^{\Delta\Delta}(t) + f(u(\sigma(t))) = 0$, $t \in [0, 1]$, satisfying the boundary conditions, $\alpha y(0)-\beta y^\Delta(0)=0$ and $\gamma y(\sigma(1))+\delta y^\Delta ((1))=0$, where $f$ is a positive function and $f(x)$ is sublinear (respectively supcrlinear) at $x = 0$ and is superlinear (respectively sublinear) at $x = \infty$· The methods involve applications of a fixed point theorem for operators on a cone in a Banach space.

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*Tamkang Journal of Mathematics*,

*30*(3), 231–240. https://doi.org/10.5556/j.tkjm.30.1999.4230

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