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UNIQUENESS OF POSITIVE SOLUTIONS FOR NONLINEAR BOUNDARY VALUE PROBLEMS IN TIME SCALES

Chien-Hsiung Lin

Abstract


Sufficient conditions for the uniqueness of positive solutions for nonlinear
boundary value problems in time scales
$$
{\hbox{\rm (BVP)}}\qquad
\left\{
\begin{array}{ll}
&(E)~~ (r(t)u^{\Delta})^{\Delta}+f(t,u^{\sigma}(t))=0,~~~~~\hbox{in}~~~~~(\theta_1,\theta_2),\\
&(BC)~~\left\{\begin{array}{lll}
&\alpha_1 u(\theta_1)-\beta_1 u^{\Delta}(\theta_1)=0,\\
&\alpha_2 u(\sigma^2(\theta_2))+\beta_2 u^{\Delta}(\sigma(\theta_2))=0
\end{array}
\right.
\end{array}
\right.
$$
\noindent
are established,where $\alpha_i, \beta_i \ge 0$ and ${\alpha_i}^2+{\beta_i}^2 \ne 0$ ~~~~~($i=1,2$).}

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