A compactness embedding lemma, a principle of symmetric criticality and applications to elliptic problems

Daniel C. De Morais, Marco Aurelio S. Souto, Joao Marcos do Ó

Resumen



Palabras clave


Compact embeding; critical Sobolev exponents; Palais-Smale condition and mountain-pass theorem; elliptic systems; incrustación compacta; exponentes críticos de Sobolev; condición de Palais-Smale; teorema del paso de montaña; sistemas elípticos.

Texto completo:

PDF

Referencias


C. O. Alves, Existência de solucoes positivas de equacoes elípticas nao-lineares variacionais em RN; Tese de Doutorado, Universidade de Brasília, Brasil, (1995)

C.O. Alves - J. V. Goncalves - O. H. Miyagaki, Multiple positive solutions for semilinear elliptic equations in RN involving critical exponents. preprint (1996)

Alves, C.O; D. C. de Morais Filho & M. A. S. Souto, On a system of elliptic equations with subcritical Sobolev exponent, Proceedings of the 450 Seminário Brasileiro de Análise- Florianópolis Brasil (1997)

J. G. Azorero - I. P. Alonzo, Existence and nonuniqueness for pLaplacian: nonlinear eigenvalues, Comm. in Partial Differential Equations 12(12), pp. 1389-1430 (1987).

J. G. Azorero - I. P. Alonzo, Problemas elípticos no lineales con exponentes críticos: falta de compacidad

J. G. Azorero - I. P. Alonzo, Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term, Transactions of the AMS, Vol. 323, No. 2, Feb, pp. 877-895, (1991).

V. Benci - G. Cerami, Existence of positive solutions of the equations ∆u + a(x)u = u N N− +2 2 in RN, J. Funct. Anal. 88, pp. 90-117, (1990).

H. Berestycki - P. L. Lions, Une methode locale pour l’existence de solutions positives de problemes semi-lineaires elliptiques dans RN, Journal D’Analyse Mathématique, vol. 38 , pp. 144 - 187, (1980).

H. Brezis - E. Lieb, A relation between pointwise convergence of functions and convergence functional, Proc. Amer. Math. Cos. 88, pp. 486-490, (1983).

H. Brezis - L. Nirenberg, Some variational problems with lack of compactness, Proc. Symp. Pure Math. (AMS) 45, pp. 165-201, (1986).

H. Brezis - L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponent, Comm. Pure and Appl. Math. 36, pp. 437-477, (1983).

D. G. Costa, On a nonlinear elliptic problem, preprint, (1993).

Y. Ding and S. Li, Existence of Solutions for Some Superlinear or Sublinear Elliptic Systems on RN, preprint (1993).

H. Egnell, Semilinear elliptic equations involving critical Sobolev exponents, Arch. Rat. Mech. Anal. 104, pp. 27-56, (1988).

H. Egnell, Existence and nonexistence results for m-Laplace equations involving critical Sobolev exponents, Arch. Rat. Mech. Anal. 104, pp. 57-77, (1988).

H. Egnell, Elliptic boundary value problems with singular coefficients and critical nonlinearities, Indiana Univ. Math. Journal, Vol. 38, No. 2, pp. 235-251, (1989).

Kavian O., Introducion a théorie des points critiques et applications aux problemes elliptiques, Universite de Nancy, (1993).

P. L. Lions, Symétrie et compacité dans les espaces de Sobolev, Journal of Functional Analysis 49, pp. 315-334 (1982).

O. Miyagaki, On a class of semilinear elliptic problems in RN with critical growth, CMS Technical Report # 94-12, Univ. Winscosin (1994).

J. Mawhin - M. Willem, Critical point theory and Hamiltonian systems. Springer Verlag, Berlin (1989).

W. Omana and M. Willem, Homoclinic Orbits for a Class of Hamiltonian Systems, Diff. and Int. Eq. 5, pp. 1115-1120.

R. S. Palais, The principle of Symmetric Criticality, Mathematical Physics (1979).

P. H. Rabinowitz, On a Class of nonlinear Schödinger equations, ZAMP 43, (1992).

W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55, pp. 149-162, (1977).

G. Talenti, Best constant in Sobolev inequality, Ann. Math. 110, pp. 353-372 (1976).




DOI: http://dx.doi.org/10.22199/S0716-09172000000100001

Enlaces refback

  • No hay ningún enlace refback.