Global Bifurcation of Positive Solutions of Asymptotically Linear Elliptic Problems

Abstract

We are concerned with determining values of $\lambda$, for which there exist positive solutions of the nonlinear elliptic problem $-\mathrm{\Delta }u=\lambda a(x)f(u)\hspace{0.17em}\hspace{0.17em}\text{in}\mathrm{\Omega }$, $\partial u/\partial \mathbf{n}+b(x)g(u)=\mathrm{0}\text{on}\partial \mathrm{\Omega }.$ The proof of our main results is based upon unilateral global bifurcation theorem of López-Gómez.