Principal spectral curves for Lane–Emden fully nonlinear type systems and applications

In this paper we exploit the phenomenon of two principal half eigenvalues in context fully nonlinear Lane–Emden type systems with possibly unbounded coefficients and weights. We show that gives rise to existence spectral curves on plane. develop an anti-maximum principle, which is a novelty even for involving Laplacian operator. As applications, derive maximum principle small domains these systems, as well uniqueness positive solutions sublinear regime. Most our results are new scalar case, particular class Isaac’s operators coefficients, whose $$W^{2,\varrho }$$ regularity estimates also prove.