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http://dx.doi.org/10.4134/BKMS.b180011

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1891-1908 More about this Journal
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.
Keywords
S-shaped connected component; positive solutions; mean curvature operator; Minkowski space; bifurcation;
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