Second and higher order systems of boundary value problems.

*(English)*Zbl 0744.34024The author studies some linear homogeneous boundary conditions for second and higher order systems of ordinary differential equations. The main proofs are carried out by means of topological techniques. The main result concerns a Dirichlet boundary value problem for a second order differential equation which can be singular at the end points. A careful use of some inequalities yields the possibility a Nonlinear Alternative result due to A. Granas. The results are then extended to a boundary value problem of the type \(y(0)=y'(1)=0\) and then to higher order equations with similar boundary conditions.

Reviewer: P.Zezza (Firenze)

##### MSC:

34B15 | Nonlinear boundary value problems for ordinary differential equations |

##### Keywords:

linear homogeneous boundary conditions; second and higher order systems; ordinary differential equations; topological techniques; Dirichlet boundary value problem; Nonlinear Alternative result due to A. Granas
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\textit{D. O'Regan}, J. Math. Anal. Appl. 156, No. 1, 120--149 (1991; Zbl 0744.34024)

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