$S$-shaped connected component for a nonlinear Dirichlet problem involving mean curvature operator in one-dimension Minkowski space
$S$-shaped connected component for a nonlinear Dirichlet problem involving mean curvature operator in one-dimension Minkowski space
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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 $$ \left\{ \aligned &\Big(\frac{u"}{\sqrt{1-u"^2}}\Big)"+\lambda a(x)f(u)=0,\ \ \ x\in(0,1),\\ &u(0)=u(1)=0,\\ \endaligned \right. $$ 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.
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 $$ \left\{ \aligned &\Big(\frac{u"}{\sqrt{1-u"^2}}\Big)"+\lambda a(x)f(u)=0,\ \ \ x\in(0,1),\\ &u(0)=u(1)=0,\\ \endaligned \right. $$ 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.
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