This paper investigates the existence and coexistence criteria for positive solutions of systems of quasilinear elliptic equations driven by the Φ-Laplacian operator with singular nonlinearities. The methodology combines monotonicity techniques with fixed-point arguments in ordered Banach spaces, providing a unified treatment for both cooperative and competitive interaction models.
Key findings
Establishes sharp existence criteria for single equations with strongly singular terms.
Derives sufficient conditions for coexistence states in coupled systems using topological degree theory and variational methods.
Analyzes the effects of coupling parameters on solution multiplicity.
Develops novel regularity estimates in Orlicz-Sobolev spaces.
Limitations & open questions
Strongly singular case (γ≥1) for Φ-Laplacian systems is not fully understood.
Impact of coupling terms on coexistence criteria in singular systems has not been systematically analyzed.