Principal eigenvalues and eigenfunctions to Lane-Emden systems on general bounded domains - Leite, Edir Junior Ferreira; Montenegro, Marcos (Israel journal of mathematics, 2024)
We prove the existence of at least a curve of principal eigenvalues for two-parameter Lane-Emden systems under Dirichlet boundary conditions for general bounded domains. The nonhomogeneous counterpart is also addressed. Part of the main results (Theorems 1.1–1.3) are based on some deep ideas introduced in the seminal paper [4] and on two fundamental tools, both new and of independent interest: Aleksandrov–Bakelman–Pucci estimates (Theorem 2.1) and Harnack–Krylov–Safonov inequalities (Theorem 5.1) associated to Lane–Emden systems in smooth domains.