• CHUAN-JEN CHYAN Department of Mathematics, Tarnkang University, Taipei, Taiwan, 251
  • JOHNNY HENDERSON Department of Mathematics, Auburn University, Auburn, Alabama 36849-5310 USA.
  • HUI-CHUN LO Department of Mathematics, Tamkang University, Taipei, Taiwan, 251.




Differential equation, measure chain, boundary value problem


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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How to Cite

CHYAN, C.-J., HENDERSON, J., & LO, H.-C. (1999). POSITIVE SOLUTIONS IN AN ANNULUS FOR NONLINEAR DIFFERENTIAL EQUATIONS ON A MEASURE CHAIN. Tamkang Journal of Mathematics, 30(3), 231–240. https://doi.org/10.5556/j.tkjm.30.1999.4230