Abstract
A class of semilinear elliptic systems of two equations is considered. Sufficient conditions are given for the existence of different types of sign-definite solutions. These conditions relate the larger eigenvalues of certain 2 × 2 real matrices associated with the system to the first eigenvalue of − ∆ under the homogeneous Dirichlet boundary condition. A special case provides a complementary result to some of the recent works.
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