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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.
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참고문헌 (24)
참고문헌 신청
L. J. Alas / 2001 / On the Gaussian curvature of maximal surfaces and the Calabi-Bernstein theorem / Bull. London Math. Soc 33(4):454~458
R. Bartnik / 1982 / Spacelike hypersurfaces with prescribed boundary values and mean curvature / Comm. Math. Phys 87(1):131~152
C. Bereanu / 2013 / Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space / J. Funct. Anal 264(1):270~287
C. Bereanu / 2013 / Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space / J. Funct. Anal 265(4):644~659
C. Bereanu / 2007 / Existence and multiplicity results for some nonlinear prob-lems with singular Φ-Laplacian / J. Differential Equations 243(2):536~557
R. Bartnik / 1982 / Spacelike hypersurfaces with prescribed boundary values and mean curvature / Comm. Math. Phys 87(1):131~152
C. Bereanu / 2013 / Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space / J. Funct. Anal 264(1):270~287
C. Bereanu / 2013 / Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space / J. Funct. Anal 265(4):644~659
C. Bereanu / 2007 / Existence and multiplicity results for some nonlinear prob-lems with singular Φ-Laplacian / J. Differential Equations 243(2):536~557
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