On a result of C. V. Coffman and W. K. Ziemer about the prescribed mean curvature equation. (English) Zbl 1306.35050
Summary: We produce a detailed proof of a result of C. V. Coffman and W. K. Ziemer [SIAM J. Math. Anal. 22, No. 4, 982–990 (1991; Zbl 0741.35010)] on the existence of positive solutions of the Dirichlet problem for the prescribed mean curvature equation
\[
-\operatorname{div}(\nabla u/\sqrt{1+|\nabla u|^2)}=\lambda f(x,u)\,\,\text{in}\,\,\Omega, \qquad u=0\,\,\text{on}\,\,\partial\Omega,
\]
assuming that \(f\) has a superlinear behaviour at \(u=0\).
MSC:
35J93 | Quasilinear elliptic equations with mean curvature operator |
35J20 | Variational methods for second-order elliptic equations |
35J25 | Boundary value problems for second-order elliptic equations |
35J60 | Nonlinear elliptic equations |
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
35B09 | Positive solutions to PDEs |