## On a third order nonlinear boundary value problem at resonance.(English)Zbl 0847.34026

The existence of solutions to a third order boundary value problem of the form $$x'''+ x'+ g(x, x')= p(t)$$, $$x' (0)= x' (\pi)= x(\eta) =0$$, $$0\leq \eta\leq \pi$$, is proved and some further results and examples are given.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations

### Keywords:

third order boundary value problem
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