Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 09, pp. 1-14.

Title: Multiple solutions to some singular nonlinear Schrodinger equations

Author: Monica Lazzo (Univ. di Bari, Italy)
          
Abstract: 
 We consider the equation
 $$ - h^2 \Delta u + V_\varepsilon(x) u = |u|^{p-2} u $$ 
 which arises in the study of standing waves of a nonlinear 
 Schrodinger equation. We allow the potential $V_\varepsilon$ to be 
 unbounded below and prove existence and multiplicity results 
 for positive solutions.
 
 
Submitted October 3, 2000. Published January 22, 2001.
Math Subject Classifications: 35Q55, 35J20, 58E05.
Key Words: nonlinear Schrodinger equations; singular potentials; 
           variational methods; Ljusternik--Schnirelman category.