Eigenvalues of elliptic systems with different order operators

PINASCO, J. P.

Advances in mathematics research

Nova Science Pub.

Año: 2009; p. 183 - 200

In this work we study the eigenvalues of a resonant nonlinear system of partial differential equations of different orders.For a system with a second and a fourth order coupled differential equations, we show the existence of infinitely many eigenvalues, which are obtained by a variational method. We also consider a two parameter problem where each equation has a different eigenvalue parameter, and we prove the existence of a family of continuous and decreasing curves in the spectra.Also, we introduce the spectral counting function defined as the number of eigenvalues less than or equal to a given value, and we find asymptotic bounds of it growth. We prove that this function can be bounded by below (resp., by above) using the spectral counting function of a single equation of second (resp. fourth) order. We deduce from those results some lower and upper bounds of eigenvalues.