Nonresonance and existence for systems of nonlinear operator equations


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.


Dezideriu Muzsi
Department of Applied Mathematics , Babeş–Bolyai University , Cluj, Romania

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


non-linear operator equation; non-linear system; fixed point; non resonance; eigenvalues; energetic norm; elliptic system.

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D. Muzsi, R. Precup, Nonresonance and existence for systems of nonlinear operator equations, Appl. Anal. 87 (2008), no. 9, 1005-1018,


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