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.


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