EXISTENCE OF NONTRIVIAL NONNEGATIVE WEAK SOLUTIONS FOR A CLASS OF LOGISTIC-TYPE SYSTEMS

Abstract

We consider the following logistic system 1122(,,)(,) in ,(,,)(,) in ,0,0 on .ppufxuvgxuvfxvugxvuvλλ−Δ=−Ω
 −Δ=−Ω
 ==∂Ω
Assuming that the nonlinearities if and ig satisfy certain growth conditions. We use the fixed point index theory and monotone minorants techniques to prove the existence of solutions for the system. This extends some known results.