×

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

References:

[1] SCHMITT K.: A nonlinear boundary value problem. J. Diff. Equat., 7, 1970, 527-537. · Zbl 0198.12301 · doi:10.1016/0022-0396(70)90099-9
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.