## Advanced differential equations with nonlinear boundary conditions.(English)Zbl 1092.34032

Consider the nonlinear boundary value problem $x'(t)=f(t, c(t),x( \alpha(t))), \quad 0= g(x(0),x(T))\tag{*}$ under the assumption that $$f,\alpha$$ and $$g$$ are continuous functions with $$b\leq \alpha(t)\leq T$$. By means of the method of monotone iteration based on lower and upper solutions for (*), the author derives sufficient conditions for (*) to have an extremal solution or a unique solution. Linear advanced differential inequalities are discussed, too.

### MSC:

 34K10 Boundary value problems for functional-differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations
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### References:

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