Finite difference reaction diffusion equations with nonlinear boundary conditions

1995 ◽  
Vol 11 (4) ◽  
pp. 355-374 ◽  
Author(s):  
C. V. Pao
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

scholarly journals Bifurcation from infinity for reaction–diffusion equations under nonlinear boundary conditions

2017 ◽  
Vol 147 (3) ◽  
pp. 649-671
Author(s):  
Nsoki Mavinga ◽  
Rosa Pardo
Keyword(s):  
Maximum Principle ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotically Linear ◽  
Bifurcation From Infinity

We consider reaction–diffusion equations under nonlinear boundary conditions where the nonlinearities are asymptotically linear at infinity and depend on a parameter. We prove that, as the parameter crosses some critical values, a resonance-type phenomenon provides solutions that bifurcate from infinity. We characterize the bifurcated branches when they are sub- or supercritical. We obtain both Landesman–Lazer-type conditions that guarantee the existence of solutions in the resonant case and an anti-maximum principle.

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