Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in \(\mathbb R^3\). (English) Zbl 1144.35382
Under some conditions on \(f(u)\), we show that for small, the only solutions to the following elliptic equation \(\Delta u \lambda u + f(u) = 0\) in \(\Omega u>0\) in \(\Omega\) and \(\partial /\partial v = 0\) on \(\partial \Omega\), is
constant.
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35B45 | A priori estimates in context of PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35B33 | Critical exponents in context of PDEs |
