| Abstract: |
| The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation
with nonlinear boundary conditions is considered using several new abstract
bifurcation theorems. The existence and stability of positive steady state solutions are
proved using a unified approach. The general results are applied to a Laplace equation
with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation
with superlinear nonlinearity and sublinear boundary conditions. |
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