Asymptotic Behavior of the Solutions of Linear and Quasilinear Elliptic Equations on R
نویسنده
چکیده
We investigate the relationship between the decay at infinity of the right-hand side f and solutions u of an equation Lu = f when L is a second order elliptic operator on RN . It is shown that when L is Fredholm, u inherits the type of decay of f (for instance, exponential, or power-like). In particular, the generalized eigenfunctions associated with all the Fredholm eigenvalues of L, isolated or not, decay exponentially. No use is made of spectral theory. The result is next extended when L is replaced by a Fredholm quasilinear operator. Various generalizations to other unbounded domains, higher order operators or elliptic systems are possible and briefly alluded to, but not discussed in detail.
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