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A new existence theorem for right focal boundary value problems on a measure chain. (English) Zbl 1074.34017
Summary: We consider the following differential equation on a measure chain \(\mathbb{T}\) \[ u^{\Delta\Delta}(t)+ f(u(\sigma(t)))= 0,\quad t\in [a,b]\cap \mathbb{T}, \] satisfying the right focal boundary value conditions \(u(a)= 0= u^\Delta(\sigma(b))\).
An existence result is obtained by using a fixed-point theorem due to Krasnosels’kii and Zabreiko. Our conditions imposed on \(f\) are very easy to verify and our result is even new for special cases of differential equations and difference equations, as well as in the general time scale setting.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
39A10 Additive difference equations
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