Multjparameter nonlinear eigenvalue problems: positive solutions to elliptic lotka-volterra systems

Abstract

In this paper we prove the existence of positive solutions in each component to elliptic Lotka-Volterra systems on bounded domains of Rⁿ with homogeneous Dirichlet boundary conditions. To this end, we provide an abstract framework including both local and global results in multiparameter nonlinear eigenvalue problems

Keywords:

• Nonlinear eigenvalue problems
• Lotka-Volterra systems

AMS(MOS)::

• 58E07
• 34B25