1.Department of Mathematics,Xuzhou Normal University,Xuzhou,People’s Republic of China;2.Department of Mathematics,National University of Ireland,Galway,Ireland
Abstract:
In this paper we investigate the existence of unbounded maximal subcontinua of positive solution sets of some nonlinear operator
equations that bifurcates from infinity. The main feature of the paper is that the nonlinearity may not be of asymptotically
linear type and may not be positone. The methods used to show our main results are different from that of Rabinowitz’ well-known
global bifurcation theorems and that of some other related papers. We first obtain a sequence of unbounded subcontinua located
in a pipe that bifurcates from nontrivial solutions by using a topological degree argument. Then using a result on subcontinua
of superior limit in metric spaces we obtain the main results concerning unbounded maximal subcontinua of positive solution
sets of the nonlinear operator equation. The main results can be applied to the semipositone problems to obtain the existence
of positive solutions.