## Existence theorems for a certain nonlinear boundary value problem of the third order.(English)Zbl 0631.34022

The author investigates the following boundary value problem: $x\prime''=f(t,x,x',x''),\quad \alpha_ 2x'(a_ 1)-\alpha_ 3x''(a_ 1)=A_ 1,\quad x(a_ 2)=A_ 2,\quad y_ 2x'(a_ 3)+\gamma_ 3x''(a_ 3)=A_ 3.$ Existence theorems for a solution, which lies between the lower and upper solutions of the problem, are proved.

### MSC:

 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations
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### References:

 [1] SCHMITT K.: A nonlinear boundary value problem. J. Diff. Equat., 7, 1970, 527-537. · Zbl 0198.12301 [2] HARTMAN P.: Obvyknovennyje diferenciaľnyje uravnenija. Izdat. MIR, Moskva 1970, [3] RUSNÁK J.: A three-point boundary value problem for third order differential equations. Math. Slovaca 33, 1983, 307-320. · Zbl 0526.34012
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