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arXiv · 1503.01807

Non-spurious solutions to discrete boundary value problems through variational methods

Marek Galewski·Ewa Schmeidel
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Abstract

Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[ 0,1\right] \times \mathbb{R} \rightarrow \mathbb{R}$ is a jointly continuous function convex in $x$ which does not need to satisfy any further growth conditions.

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Marek Galewski, Ewa Schmeidel. 2015-03-05. Non-spurious solutions to discrete boundary value problems through variational methods. https://arxiv.org/abs/1503.01807

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