Geodesic
Multiple solutions to some singular nonlinear Schrödinger equations
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a4/}
}
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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/