MULTIPLE POSITIVE SOLUTIONS OF CONJUGATE BOUNDARY VALUE PROBLEMS ON TIME SCALES

Abstract

We consider the following differential equation on a time scale $T$ \[ y^{\Delta \Delta}(t) + P(t, y(\sigma(t))) = 0, \; t \in [a,b] \cap T \] subject to conjugate boundary conditions \[ y(a) = 0, \qquad y(\sigma^{2}(b)) = 0 \] where $a,b \in T$ and $a \lt \sigma(b)$. By using different fixed point theorems, criteria are established for the existence of three positive solutions of the boundary value problem. Examples are also included to illustrate the results obtained.