Existence of multiple positive solutions for second order nonlinear dynamic BVPs by variational methods. (English) Zbl 1126.34018

The authors have employed variational techniques and critical point theory to obtain sufficient conditions for the existence of multiple positive solutions of second order dynamic equations with homogeneous Dirichlet boundary conditions of the form
\[ -u^{\Delta\Delta}(t)=f(t,u^\sigma(t)),\quad t\in J\cap T^{k^2},\quad u(a)=0=u(b), \]
\[ J=\begin{cases} [a,b)\cap T &\text{if }a<\sigma(a)\\ (a,b)\cap T &\text{if }a=\sigma(a), \end{cases} \] \(T\subset \mathbb R\) an arbitrary bounded time scale such that \(\min T= a\) and \(\max T= b\) and \(f:J\times\mathbb R\to\mathbb R\).


34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
39A10 Additive difference equations
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