# S-SHAPED CONNECTED COMPONENT FOR A NONLINEAR DIRICHLET PROBLEM INVOLVING MEAN CURVATURE OPERATOR IN ONE-DIMENSION MINKOWSKI SPACE

• Ma, Ruyun (Department of Mathematics Northwest Normal University) ;
• Xu, Man (Department of Mathematics Northwest Normal University)
• Accepted : 2018.08.16
• Published : 2018.11.30

#### Abstract

In this paper, we investigate the existence of an S-shaped connected component in the set of positive solutions of the Dirichlet problem of the one-dimension Minkowski-curvature equation $$\{$\frac{u^{\prime}}{\sqrt{1-u^{{\prime}2}}}$^{\prime}+{\lambda}a(x)f(u)=0,\;x{\in}(0,1),\\u(0)=u(1)=0$$, where ${\lambda}$ is a positive parameter, $f{\in}C[0,{\infty})$, $a{\in}C[0,1]$. The proofs of main results are based upon the bifurcation techniques.

#### Acknowledgement

Supported by : NSFC

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