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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References:

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