Asymptotics for Semilinear Field Equations with Slowly Decaying Mass

WKB Asymptotic Behavior of Almost All Ge

WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for One-Dimensional Schrödinger Operators with Slowly Decaying Potentials

✍ Michael Christ; Alexander Kiselev 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 192 KB

We prove the WKB asymptotic behavior of solutions of the differential equation &d 2 uÂdx 2 +V(x) u=Eu for a.e. E>A where V=V 1 +V 2 , V 1 # L p (R), and V 2 is bounded from above with A=lim sup x Ä V(x), while V$ 2 (x) # L p (R), 1 p<2. These results imply that Schro dinger operators with such poten