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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 $b\le \alpha(t)\le T$. 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.

34K10Boundary value problems for functional-differential equations
34A45Theoretical approximation of solutions of ODE
Full Text: DOI
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