Geodesic
Multiple solutions to some singular nonlinear Schrödinger equations
Electronic journal of differential equations, Tome 2001 (2001)
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.
Classification : 35Q55, 35J20, 58E05
Keywords: nonlinear Schrödinger equations, singular potentials, variational methods, Ljusternik--schnirelman category 
@article{EJDE_2001__2001__a4,
     author = {Lazzo,  Monica},
     title = {Multiple solutions to some singular nonlinear {Schr\"odinger} equations},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0964.35141},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a4/}
}
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%A Lazzo,  Monica
%T Multiple solutions to some singular nonlinear Schrödinger equations
%J Electronic journal of differential equations
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Lazzo,  Monica. Multiple solutions to some singular nonlinear Schrödinger equations. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a4/