Bifurcation Asymptotic profiles Nonlocal diffusion Elliptic semilinear systems of competitive type Logistic problems Sub- and supersolutions Boundary blow-up Eigenvalues and eigenfunctions Elliptic equations Elliptic problems Elliptic systems Nonlinear boundary conditions Principal eigenvalues 35S15 45M20 47G10 A Priori Estimates A priori bounds A priori estimates Antimaximum principle Asymptotic behaviors Boundary layers Bounded domain Compactly supported Concave-convex Dependence on parameters Diffusion Dirichlet problem Eigenvalues Elliptic problem