On nodal radial solutions of an elliptic problem involving critical Sobolev exponent

Jan H. Chabrowski

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 1, page 1-16
  • ISSN: 0010-2628

Abstract

top
In this paper we construct radial solutions of equation (1) (and (13)) having prescribed number of nodes.

How to cite

top

Chabrowski, Jan H.. "On nodal radial solutions of an elliptic problem involving critical Sobolev exponent." Commentationes Mathematicae Universitatis Carolinae 37.1 (1996): 1-16. <http://eudml.org/doc/247913>.

@article{Chabrowski1996,
abstract = {In this paper we construct radial solutions of equation (1) (and (13)) having prescribed number of nodes.},
author = {Chabrowski, Jan H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {elliptic equations; radial solutions; critical Sobolev exponent; mountain pass theorem; prescribed number of nodes; Nehari manifold; potential operator equations},
language = {eng},
number = {1},
pages = {1-16},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On nodal radial solutions of an elliptic problem involving critical Sobolev exponent},
url = {http://eudml.org/doc/247913},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Chabrowski, Jan H.
TI - On nodal radial solutions of an elliptic problem involving critical Sobolev exponent
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 1
SP - 1
EP - 16
AB - In this paper we construct radial solutions of equation (1) (and (13)) having prescribed number of nodes.
LA - eng
KW - elliptic equations; radial solutions; critical Sobolev exponent; mountain pass theorem; prescribed number of nodes; Nehari manifold; potential operator equations
UR - http://eudml.org/doc/247913
ER -

References

top
  1. Adimurthi, Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the n -Laplacian, Ann. Scuola Norm. Sup. Pisa 12.1 (1990), 393-413. (1990) Zbl0732.35028MR1079983
  2. Ambrosetti A., Rabinowitz P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381. (1973) Zbl0273.49063MR0370183
  3. Bartsch Th., Willem M., Infinitely many radial solutions of a semilinear elliptic problem on N , Arch. Rat. Mech. Anal. 124 (1993), 261-274. (1993) MR1237913
  4. Bianchi G., Chabrowski J., Szulkin A., On symmetric solutions of an elliptic equation involving critical Sobolev exponent, Nonlinear Analysis, TMA 25(1) (1995), 41-59. (1995) MR1331987
  5. Ladyzhenskaya O.A., Ural'ceva O.A., Linear and Quasilinear Elliptic Equations, Academic Press New York (1968). (1968) MR0244627
  6. Lions P.L., Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (1982), 315-334. (1982) Zbl0501.46032MR0683027
  7. Yi Li, Wei-Ming Ni, On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in n , I Asymptotic behavior, II Radial symmetry, Arch. Rat. Mech. Anal. 118 (1992), 195-222, 223-243. (1992) MR1158935
  8. Rother W., Some existence results for the equation Δ U + K ( x ) U p = 0 , Commun. in P.D.E. 15.10 (1990), 1461-1473. (1990) MR1077474
  9. Stuart C.A., Bifurcation in L p ( N ) for a semilinear elliptic equations, Proc. London Math. Soc. 57(3) (1988), 511-541. (1988) Zbl0673.35005MR0960098
  10. Talenti G., Best constants in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353-372. (1976) MR0463908
  11. Vainberg M.M., Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, John Wiley & Sons New York-Toronto (1973). (1973) Zbl0279.47022MR0467428

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.