Multiple positive solutions for classes of elliptic systems with combined nonlinear effects.

摘要

We study positive solutions to nonlinear elliptic systems of the form: -Du=lfv inW -Dv=lgu inW u=0=von6W where u is the Laplacian of u, lambda is a positive parameter and O is a bounded domain in RN with smooth boundary ∂O. In particular, we will analyze the combined effects of the nonlinearities on the existence and multiplicity of positive solutions. We also study systems with multiparameters and stronger coupling. We extend our results to p-q-Laplacian systems and to n x n systems. We mainly use sub- and super-solutions to prove our results.