Electron. J. Diff. Eqns., Vol. 2001(2001), No. 09, pp. 1-14.

Multiple solutions to some singular nonlinear Schrodinger equations

Monica Lazzo

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.

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Monica Lazzo
Dipartimento di Matematica
Universita di Bari
via Orabona 4,
70125 Bari, Italy
e-mail: lazzo@dm.uniba.it

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