Critical groups computations on a class of Sobolev Banach spaces via Morse index

Silvia Cingolani; Giuseppina Vannella

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 2, page 271-292
  • ISSN: 0294-1449

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Cingolani, Silvia, and Vannella, Giuseppina. "Critical groups computations on a class of Sobolev Banach spaces via Morse index." Annales de l'I.H.P. Analyse non linéaire 20.2 (2003): 271-292. <http://eudml.org/doc/78579>.

@article{Cingolani2003,
author = {Cingolani, Silvia, Vannella, Giuseppina},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Morse theory; critical groups estimate; -Laplacian; weak solution; quasilinear elliptic equation},
language = {eng},
number = {2},
pages = {271-292},
publisher = {Elsevier},
title = {Critical groups computations on a class of Sobolev Banach spaces via Morse index},
url = {http://eudml.org/doc/78579},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Cingolani, Silvia
AU - Vannella, Giuseppina
TI - Critical groups computations on a class of Sobolev Banach spaces via Morse index
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 2
SP - 271
EP - 292
LA - eng
KW - Morse theory; critical groups estimate; -Laplacian; weak solution; quasilinear elliptic equation
UR - http://eudml.org/doc/78579
ER -

References

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  1. [1] Arcoya D., Boccardo L., Critical points for multiple integrands of the calculus of variations, Arch. Rat. Mech. Anal.134 (1996) 249-274. Zbl0884.58023MR1412429
  2. [2] Benci V., D'Avenia P., Fortunato D., Pisani L., Solitons in several space dimensions: a Derrick's problem and infinitely many solutions, Arch. Rat. Mech. Anal.154 (2000) 297-324. Zbl0973.35161MR1785469
  3. [3] Benci V., Fortunato D., Pisani L., Soliton-like solutions of a Lorentz invariant equation in dimension 3, Math. Phys.3 (1998) 315-344. Zbl0921.35177MR1626832
  4. [4] Chang K., Morse theory on Banach space and its applications to partial differential equations, Chin. Ann. of Math.4B (1983) 381-399. Zbl0534.58020MR742038
  5. [5] Chang K., Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993. Zbl0779.58005MR1196690
  6. [6] Chang K., Morse theory in nonlinear analysis, in: Ambrosetti A., Chang K.C., Ekeland I. (Eds.), Nonlinear Functional Analysis and Applications to Differential Equations, Word Scientific, Singapore, 1998. Zbl0960.58006MR1703528
  7. [7] Cingolani S., Vannella G., Some results on critical groups for a class of functionals defined on Sobolev Banach spaces, Rend. Acc. Naz. Lincei12 (2001) 1-5. Zbl1072.58005MR1898461
  8. [8] Corvellec J.N., Degiovanni M., Nontrivial solutions of quasilinear equations via nonsmooth Morse theory, J. Differential Equations136 (1997) 268-293. Zbl1139.35335MR1448826
  9. [9] Dibenedetto E., C1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis TMA7 (1983) 827-850. Zbl0539.35027
  10. [10] Egnell H., Existence an nonexistence results for m-Laplace equations involving critical Sobolev exponents, Arch. Rat. Mech. Anal.104 (1988) 57-77. Zbl0675.35036MR956567
  11. [11] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1998. Zbl1042.35002
  12. [12] Ioffe A.D., On lower semicontinuity of integral functionals I and II, SIAM J. Control Optim.15 (1977) 521-538, and 991–1000. Zbl0361.46037MR637234
  13. [13] Ladyzhenskaya O.A., Ural'tseva N.N., Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
  14. [14] Lancelotti S., Morse index estimates for continuous functionals associated with quasilinear elliptic equations, Adv. Differential Equations7 (2002) 99-128. Zbl1035.58010MR1867706
  15. [15] Mawhin J., Willem M., Critical Point Theory and Hamiltonian Systems, Applied Mathematical Sciences, 74, Springer-Verlag, New York, 1989. Zbl0676.58017MR982267
  16. [16] Mercuri F., Palmieri G., Problems in extending Morse theory to Banach spaces, Boll. UMI12 (1975) 397-401. Zbl0323.58009MR405494
  17. [17] Palais R., Morse theory on Hilbert manifolds, Topology2 (1963) 299-340. Zbl0122.10702MR158410
  18. [18] Smale S., Morse theory and a non-linear generalization of the Dirichlet problem, Ann. Math.80 (1964) 382-396. Zbl0131.32305MR165539
  19. [19] Spanier E.H., Algebraic Topology, McGraw-Hill, New York, 1966. Zbl0145.43303MR210112
  20. [20] Tolksdorf P., Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations51 (1984) 126-150. Zbl0488.35017MR727034
  21. [21] Tolksdorf P., On the Dirichlet problem for a quasilinear equations in domains with conical boundary points, Comm. Part. Differential Equations8 (1983) 773-817. Zbl0515.35024MR700735
  22. [22] Tromba A.J., A general approach to Morse theory, J. Differential Geom.12 (1977) 47-85. Zbl0344.58012MR464304
  23. [23] Uhlenbeck K., Morse theory on Banach manifolds, J. Funct. Anal.10 (1972) 430-445. Zbl0241.58002MR377979

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