Stationary states for a two-dimensional singular Schrödinger equation

Paolo Caldiroli; Roberta Musina

Bollettino dell'Unione Matematica Italiana (2001)

  • Volume: 4-B, Issue: 3, page 609-633
  • ISSN: 0392-4041

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Caldiroli, Paolo, and Musina, Roberta. "Stationary states for a two-dimensional singular Schrödinger equation." Bollettino dell'Unione Matematica Italiana 4-B.3 (2001): 609-633. <http://eudml.org/doc/195731>.

@article{Caldiroli2001,
author = {Caldiroli, Paolo, Musina, Roberta},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {singular elliptic equations; variational methods; Hardy-Sobolev inequality; concentration-compactness principle},
language = {eng},
month = {10},
number = {3},
pages = {609-633},
publisher = {Unione Matematica Italiana},
title = {Stationary states for a two-dimensional singular Schrödinger equation},
url = {http://eudml.org/doc/195731},
volume = {4-B},
year = {2001},
}

TY - JOUR
AU - Caldiroli, Paolo
AU - Musina, Roberta
TI - Stationary states for a two-dimensional singular Schrödinger equation
JO - Bollettino dell'Unione Matematica Italiana
DA - 2001/10//
PB - Unione Matematica Italiana
VL - 4-B
IS - 3
SP - 609
EP - 633
LA - eng
KW - singular elliptic equations; variational methods; Hardy-Sobolev inequality; concentration-compactness principle
UR - http://eudml.org/doc/195731
ER -

References

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  3. BREZIS, H.- CABRÉ, X., Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. (8), 1-B (1998), 223-262. Zbl0907.35048MR1638143
  4. CAFFARELLI, L.- KOHN, R.- NIRENBERG, L., First Order Interpolation Inequalities with Weight, Compositio Math., 53 (1984), 259-275. Zbl0563.46024MR768824
  5. CALDIROLI, P.- MALCHIODI, A., Singular elliptic problems with critical growth, Comm. Part. Diff. Eq., to appear. Zbl1072.35527MR1916550
  6. CALDIROLI, P.- MUSINA, R., On the Existence of Extremal Functions for a Weighted Sobolev Embedding with Critical Exponent, Calc. Var., 8 (1999), 365-387. Zbl0929.35045MR1700269
  7. CALDIROLI, P.- MUSINA, R., Existence and non existence results for a class of nonlinear singular Sturm-Liouville equations, Adv. Diff. Eq., to appear. Zbl1032.34034
  8. CALDIROLI, P.- MUSINA, R., On a Class of 2-dimensional Singular Elliptic Problems, Proc. Roy. Soc. Edinburgh Sect. A, to appear. Zbl1005.35034MR1838499
  9. FRANK, W.- LAND, D.- SPECTOR, R., Singular Potentials, Rev. Modern Phys., 43 (1971), 36-98. MR449255
  10. JANNELLI, E.- SOLIMINI, S., Concentration estimates for critical problems, Ricerche Mat., 48 (1999), Supplemento, 233-257. Zbl0944.35022MR1765687
  11. LIONS, P.-L., The concentration-compactness principle in the calculus of variations. The Locally compact case, parts 1-2, Ann. Inst. H. Poincaré Anal. non linéaire, 1 (1984), 109-145 and 223-283. Zbl0704.49004MR778970
  12. TERRACINI, S., On positive entire solutions to a class of equations with a singular coefficient and critical exponent, Adv. Diff. Eq., 1 (1996), 241-264. Zbl0847.35045MR1364003
  13. TERTIKAS, A., Critical Phenomena in Linear Elliptic Problems, J. Funct. Anal., 154 (1998), 42-66. Zbl0920.35044MR1616516

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