Bifurcation From Infinity For Reaction–Diffusion Equations Under Nonlinear Boundary Conditions

Authors

Nsoki Mavinga, Swarthmore CollegeFollow
R. Pardo

Document Type

Article

Publication Date

6-1-2017

Published In

Proceedings Of The Royal Society Of Edinburgh Section A: Mathematics

Abstract

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.

Keywords

Steklov eigenvalues, elliptic equations, nonlinear boundary conditions, Bifurcation

Comments

This work is freely available courtesy of Cambridge University Press and the Royal Society of Edinburgh.

Recommended Citation

Nsoki Mavinga and R. Pardo. (2017). "Bifurcation From Infinity For Reaction–Diffusion Equations Under Nonlinear Boundary Conditions". Proceedings Of The Royal Society Of Edinburgh Section A: Mathematics. Volume 147, Issue 3. 649-671. DOI: 10.1017/S0308210516000251
https://works.swarthmore.edu/fac-math-stat/178