Proceedings Of The Royal Society Of Edinburgh Section A: Mathematics
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.
Steklov eigenvalues, elliptic equations, nonlinear boundary conditions, Bifurcation
Nsoki Mavinga and R. Pardo.
"Bifurcation From Infinity For Reaction–Diffusion Equations Under Nonlinear Boundary Conditions".
Proceedings Of The Royal Society Of Edinburgh Section A: Mathematics.