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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
##### Keywords:
Measure chain; Positive solution; Fixed-point theorem
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##### References:
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