Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 264, Issue 1, Pages 425-454Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2017.09.014
Keywords
Reaction-diffusion equation; Nonlinear boundary condition; Bifurcation; Stability
Categories
Funding
- NSFC [11571086]
- NSF [DMS-1313243]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1313243] Funding Source: National Science Foundation
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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. (C) 2017 Elsevier Inc. All rights reserved.
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