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

  • CLAUDIANOR O. ALVES (a1), ANGELO R. F. DE HOLANDA (a1) and JOSÉ A. FERNANDES (a1)

Abstract

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.

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References

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1.Alves, C. O., Existência de solução positiva de Equações não-lineares variacionais em N, Doct. Dissertation (University of Brasilia, UnB, 1996).
2.Alves, C. O., Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian, Nonlinear Anal. 51 (2002), 11871206.
3.Alves, C. O., Positive solutions to quasilinear equations involving critical exponent on perturbed annular domains, Eletr. J. Diff. Equations 2005 (13) (2005), 113.
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), 611624.
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), 722755.
6.Benci, V. and Cerami, G., Existence of positive solutions of the equation in N, J. Funct. Anal. 88 (1990), 91117.
7.Ben-Naoum, A., Troestler, C. and Willem, M., Extrema problems with critical exponents on unbounded domain, Nonlinear Anal. 26 (1996), 823833.
8.Brezis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 486490.
9.Cerami, G. and Passaseo, D., Nonminiminzing positive solutions for equation with critical exponents in the half-space, SIAM J. Math. Anal. 28 (1997), 867885.
10.Chabrowski, J. and Yang, J., Multiple semiclassical solutions of the Schrodinger equation involving a critical Sobolev exponent, Portugaliae Mathematica 57 (3) (2000), 273284.
11.Chen, Y., Levine, S. and Rao, M., Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (4) (2006), 13831406.
12.de Medeiros, E. S., Existência e concentração de solução para o p-Laplaciano com condições de Neumann, Doctoral Dissertation (UNICAMP, 2001).
13.DiBenedetto, E., C 1 + α Local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827850.
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), 703726.
15.Egnell, H., Existence and non-existence results for m-Laplace equations involving critical Sobolev exponents, Arch. Rational Mech. Anal. 104 (1988), 5777.
16.Garcia Azorero, J. and Peral Alonso, I., Existence and nonuniqueness for the p-Laplacian: Nonlinear Eigenvalue, Comm. PDE 12 (1987), 13891490.
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), 877895.
18.Gueda, M. and Veron, L., Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA 13 (1989), 419431.
19.Lions, P. L., The concentration–compactness principle in the calculus of variations: The limit case, Rev. Mat. Iberoamericana 1 (1985), 145201.
20.Noussair, E. S., Swanson, C. A. and Yang, J., Quasilinear elliptic problems with critical exponents, Nonlinear Anal. Math. Appl. 20 (3) (1993), 285301.
21.Passaseo, D., Some sufficient conditions for the existence of positive solutions to the equation , Ann. Ins. Henri Poincaré 13 (1996), 185227.
22.Struwe, M., A global compactness results for elliptic boundary value problem involving limiting nonlinearities, Math. Z. 187 (1984), 511517.
23.Talenti, G., Best constant in Sobolev inequality, Ann. Math. 110 (1976), 353372.
24.Tarantello, G., Multiplicity results for an inhomogeneous Neumann problem critical exponent, Manuscripta Math. 81 (1993), 5778.
25.Wang, X. J., Neumann problem of semilinear elliptic equations involving critical Sobolev exponent, J. Differential Equations 93 (1991), 283310.

Keywords

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

  • CLAUDIANOR O. ALVES (a1), ANGELO R. F. DE HOLANDA (a1) and JOSÉ A. FERNANDES (a1)

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