On a Class of Asymptotically Linear Schrodinger Equations in R^N.
by
David Costa
Univ of Nevada - Las Vegas

We consider the question of existence of solution for the Schrodinger equation

-\Deltau + V(x) u + g(x, u) = f(x) ,   in  RN ,

where the potential V(x) satisfies lim_{|x| --> \infty}V(x)=0 and g(x, s) is a "jumping nonlinearity" in the sense that the limits lim_{s --> -\infty}\fracg(x, s)s=a, lim_{s --> +\infty}\fracg(x, s)s=b exist and "jump" over an eigenvalue of \Delta- V(x). For suitable a < b and we show that a solution u in H² (R^N) exists for any given f in L² (R^N). This is joint work with H. Tehrani.

Date received: May 21, 2002