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.


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