Multiplicity results for system of Pucci's extremal operator

This article deals with the existence of multiple positive solutions to the following system of nonlinear equations involving Pucci's extremal operators: { -M+lambda 1,Lambda 1(D2u1)=f1(u1,u2,...,un) in Omega -M+lambda 2,Lambda 2(D2u2)=f2(u1,u2,...,un) in Omega .=... -M+lambda n,Lambda n(D2un)=fn(u1,u2,...,un) in Omega, u1=u2= <middle dot><middle dot><middle dot> =un=0 on partial derivative Omega where Omega is a smooth and bounded domain in R-N and fi:[0,infinity)x[0,infinity)<middle dot><middle dot><middle dot> x[0,infinity)->[0,infinity)are C alpha functions fori=1,2,...,n. The multiplicity result in this work is motivated by the work Amann (SIAM Rev 18(4):620-709, 1976), and Shivaji (Nonlinear analysis and applications (Arlington, Tex., 1986), Dekker, NewYork, 1987), where the three solutions theorem (multiplicity) has been proved for linear equations. Later on, it was extended for a system of equations involving the Laplace operator by Shivaji and Ali (Differ Integr Equ 19(6):669-680, 2006). Thus, the results here can be considered as a nonlinear analog of the results mentioned above. We also have applied the above results to show the existence of three positive solutions to a system of nonlinear elliptic equations having combined sublinear growth by explicitly constructing two ordered pairs of sub and super solutions