### Multiplicity of solutions for asymptotically linear $n$-th order boundary value problems

DOI: http://dx.doi.org/10.12775/TMNA.2007.019

#### Abstract

In this paper we investigate existence and multiplicity of solutions, with

prescribed nodal properties, to a two-point boundary value problem of

asymptotically linear $n$-th order equations. The proof follows a shooting

approach and it is based on the weighted eigenvalue theory for linear $n$-th

order boundary value problems.

prescribed nodal properties, to a two-point boundary value problem of

asymptotically linear $n$-th order equations. The proof follows a shooting

approach and it is based on the weighted eigenvalue theory for linear $n$-th

order boundary value problems.

#### Keywords

n-th order problem; asymptotically linear; multiplicity results; shooting approach; weighted eigenvalues

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