Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the n -laplacian

Adimurthi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)

  • Volume: 17, Issue: 3, page 393-413
  • ISSN: 0391-173X

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Adimurthi. "Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the $n$-laplacian." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.3 (1990): 393-413. <http://eudml.org/doc/84080>.

@article{Adimurthi1990,
author = {Adimurthi},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3},
pages = {393-413},
publisher = {Scuola normale superiore},
title = {Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the $n$-laplacian},
url = {http://eudml.org/doc/84080},
volume = {17},
year = {1990},
}

TY - JOUR
AU - Adimurthi
TI - Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the $n$-laplacian
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 3
SP - 393
EP - 413
LA - eng
UR - http://eudml.org/doc/84080
ER -

References

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  1. [1] Adimurthi, Positive solutions of the semilinear Dirichlet problem with Critical growth in the unit disc in R2, Proc. Indian Acad. Sci., 99, (1989), pp. 49-73. Zbl0681.35032
  2. [2] F.V. Atkinson - L.A. Peletier, Ground states and Dirichlet problems for -Δu=f(u) in R2, Archive for Rational Mechanics and Analysis, No. 2, 96 (1986), pp. 147-165. Zbl0657.35057
  3. [3] H. Brezis, Nonlinear elliptic equations involving the Critical Sobolev exponent- Survey and perspectives, Directions in partial differential equations, Ed. Crandall etc. (1987), pp. 17-36. Zbl0699.35075
  4. [4] H. Brezis - L. Nirenberg, Positive solutions of non-linear elliptic equations involving critical Sobolev exponents, Comm Pure Appl. Maths, 36 (1983), pp. 437-477. Zbl0541.35029
  5. [5] P. Cherrier, Problems de Neumann non lineaires sur les varietes riemanniennes, C.R. Acad. Sc. Paris, Serie A, 292 (1984), pp. 225-262. 
  6. [6] Di Benedetto, C1,α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis - TMA, No. 8, 7 (1983), pp. 827-850. Zbl0539.35027
  7. [7] J.P. Garcia Azorero - I. Peral Alonso, Existence and non-uniqueness for the p-Laplacian, Comm in P.D.E, 12 (1987), pp. 1389-1430. Zbl0637.35069
  8. [8] D. Gilbarg - N. Trudinger, Elliptic Partial differential equations of second order, 2nd edition, Springer Verlag (1983). Zbl0562.35001
  9. [9] P.L. Lions, The Concentration Compactness principle in the calculus of variations, part-I, Revista mathematica Iberoamericana, No. 1, 1 (1985), pp. 185-201. Zbl0704.49005
  10. [10] J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Maths Jr, No. 11, 20 (1971), pp. 1077-1092. Zbl0203.43701
  11. [11] Z. Nehari, On a class of non-linear second order differential equations, Trans AMS, 95 (1960), pp. 101-123. Zbl0097.29501
  12. [12] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, Jr diff. eqs, 51 (1984), pp. 126-150. Zbl0488.35017
  13. [13] N.S. Trudinger, On imbedding into Orlicz spaces and some applications, Jr Math Mech, 17 (1967), pp. 473-484. Zbl0163.36402

Citations in EuDML Documents

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  1. Jan H. Chabrowski, On nodal radial solutions of an elliptic problem involving critical Sobolev exponent
  2. Adimurthi, S. L. Yadava, Multiplicity results for semilinear elliptic equations in a bounded domain of 2 involving critical exponents
  3. Elliot Tonkes, Solutions to a perturbed critical semilinear equation concerning the N -Laplacian in N
  4. Robert Černý, Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces
  5. Robert Černý, Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities
  6. Elves A. de B. Silva, Sérgio H. M. Soares, Liouville-Gelfand type problems for the N -laplacian on bounded domains of N
  7. Robert Černý, Concentration-Compactness Principle for embedding into multiple exponential spaces on unbounded domains
  8. Robert Černý, Generalized n -Laplacian: semilinear Neumann problem with the critical growth

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