Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-18T17:25:28.224Z Has data issue: false hasContentIssue false
  • English
  • Français

EXISTENCE OF POSITIVE SOLUTION FOR A QUASI-LINEAR PROBLEM WITH CRITICAL GROWTH IN N+

Published online by Cambridge University Press:  01 May 2009

CLAUDIANOR O. ALVES ,
ANGELO R. F. DE HOLANDA  and
JOSÉ A. FERNANDES
CLAUDIANOR O. ALVES
Affiliation:
Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística CEP: 58109-970, Campina Grande-PB, Brazil e-mail: coalves@dme.ufcg.edu.br; angelo@dme.ufcg.edu.br; arimat@dme.ufcg.edu.br
ANGELO R. F. DE HOLANDA
Affiliation:
Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística CEP: 58109-970, Campina Grande-PB, Brazil e-mail: coalves@dme.ufcg.edu.br; angelo@dme.ufcg.edu.br; arimat@dme.ufcg.edu.br
JOSÉ A. FERNANDES
Affiliation:
Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística CEP: 58109-970, Campina Grande-PB, Brazil e-mail: coalves@dme.ufcg.edu.br; angelo@dme.ufcg.edu.br; arimat@dme.ufcg.edu.br
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we show existence of positive solutions for a class of quasi-linear problems with Neumann boundary conditions defined in a half-space and involving the critical exponent.

Keywords

35A1535H3035B33
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009 , pp. 367 - 383
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Alves, C. O., Existência de solução positiva de Equações não-lineares variacionais em N, Doct. Dissertation (University of Brasilia, UnB, 1996).Google Scholar
2.Alves, C. O., Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian, Nonlinear Anal. 51 (2002), 1187–1206.CrossRefGoogle Scholar
3.Alves, C. O., Positive solutions to quasilinear equations involving critical exponent on perturbed annular domains, Eletr. J. Diff. Equations 2005 (13) (2005), 1–13.Google Scholar
4.Alves, C. O. and El Hamidi, A., Nehari manifold and existence of positive solutions to a class of quasilinear problems, Nonlinear Anal. 60 (2005), 611–624.CrossRefGoogle Scholar
5.Antontsev, S. N. and Shmarev, S. I., Elliptic equations and systems with nonstandard growth conditions: Existence, uniqueness and localization properties of solutions, Nonlinear Anal. 65 (2006), 722–755.CrossRefGoogle Scholar
6.Benci, V. and Cerami, G., Existence of positive solutions of the equation in N, J. Funct. Anal. 88 (1990), 91–117.Google Scholar
7.Ben-Naoum, A., Troestler, C. and Willem, M., Extrema problems with critical exponents on unbounded domain, Nonlinear Anal. 26 (1996), 823–833.CrossRefGoogle Scholar
8.Brezis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 486–490.CrossRefGoogle Scholar
9.Cerami, G. and Passaseo, D., Nonminiminzing positive solutions for equation with critical exponents in the half-space, SIAM J. Math. Anal. 28 (1997), 867–885.CrossRefGoogle Scholar
10.Chabrowski, J. and Yang, J., Multiple semiclassical solutions of the Schrodinger equation involving a critical Sobolev exponent, Portugaliae Mathematica 57 (3) (2000), 273–284.Google Scholar
11.Chen, Y., Levine, S. and Rao, M., Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (4) (2006), 1383–1406.CrossRefGoogle Scholar
12.de Medeiros, E. S., Existência e concentração de solução para o p-Laplaciano com condições de Neumann, Doctoral Dissertation (UNICAMP, 2001).Google Scholar
13.DiBenedetto, E., C 1 + α Local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827–850.CrossRefGoogle Scholar
14.Drabek, P. and Pohozaev, S., Positive solutions for the p-Laplacian: Application of the fibering method, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), 703–726.CrossRefGoogle Scholar
15.Egnell, H., Existence and non-existence results for m-Laplace equations involving critical Sobolev exponents, Arch. Rational Mech. Anal. 104 (1988), 57–77.CrossRefGoogle Scholar
16.Garcia Azorero, J. and Peral Alonso, I., Existence and nonuniqueness for the p-Laplacian: Nonlinear Eigenvalue, Comm. PDE 12 (1987), 1389–1490.CrossRefGoogle Scholar
17.Garcia Azorero, J. and Alonso, I. Peral, Multiplicity of solutions for elliptic problems with critical exponent on with a nonsymetric term, Trans. Am. Math. Soc. 323 (1991), 877–895.CrossRefGoogle Scholar
18.Gueda, M. and Veron, L., Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA 13 (1989), 419–431.Google Scholar
19.Lions, P. L., The concentration–compactness principle in the calculus of variations: The limit case, Rev. Mat. Iberoamericana 1 (1985), 145–201.CrossRefGoogle Scholar
20.Noussair, E. S., Swanson, C. A. and Yang, J., Quasilinear elliptic problems with critical exponents, Nonlinear Anal. Math. Appl. 20 (3) (1993), 285–301.CrossRefGoogle Scholar
21.Passaseo, D., Some sufficient conditions for the existence of positive solutions to the equation , Ann. Ins. Henri Poincaré 13 (1996), 185–227.CrossRefGoogle Scholar
22.Struwe, M., A global compactness results for elliptic boundary value problem involving limiting nonlinearities, Math. Z. 187 (1984), 511–517.CrossRefGoogle Scholar
23.Talenti, G., Best constant in Sobolev inequality, Ann. Math. 110 (1976), 353–372.Google Scholar
24.Tarantello, G., Multiplicity results for an inhomogeneous Neumann problem critical exponent, Manuscripta Math. 81 (1993), 57–78.CrossRefGoogle Scholar
25.Wang, X. J., Neumann problem of semilinear elliptic equations involving critical Sobolev exponent, J. Differential Equations 93 (1991), 283–310.CrossRefGoogle Scholar