Non-resonance and existence for systems of non-linear operator equations

Abstract

An existence theory for systems of two non-linear operator equations in Hilbert spaces is presented under non-resonance conditions with respect to two spectra and in terms of matrices convergent to zero. The theory is then applied to elliptic systems.

Keywords:

• non-linear operator equation
• non-linear system
• fixed point
• nonresonance
• eigenvalues
• energetic norm
• elliptic system

2000 Mathematics Subject Classifications::

• 47J25
• 34A34
• 35J50