A saddle point approach to nonlinear eigenvalue problems

Dumitru Motreanu

Mathematica Slovaca (1997)

  • Volume: 47, Issue: 4, page 463-477
  • ISSN: 0232-0525

How to cite

top

Motreanu, Dumitru. "A saddle point approach to nonlinear eigenvalue problems." Mathematica Slovaca 47.4 (1997): 463-477. <http://eudml.org/doc/34462>.

@article{Motreanu1997,
author = {Motreanu, Dumitru},
journal = {Mathematica Slovaca},
keywords = {eigenvalue problem; critical point; semilinear elliptic equations},
language = {eng},
number = {4},
pages = {463-477},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A saddle point approach to nonlinear eigenvalue problems},
url = {http://eudml.org/doc/34462},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Motreanu, Dumitru
TI - A saddle point approach to nonlinear eigenvalue problems
JO - Mathematica Slovaca
PY - 1997
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 47
IS - 4
SP - 463
EP - 477
LA - eng
KW - eigenvalue problem; critical point; semilinear elliptic equations
UR - http://eudml.org/doc/34462
ER -

References

top
  1. AMBROSETTI A.-RABINOWITZ P. H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 369-381. (1973) Zbl0273.49063MR0370183
  2. CHANG K. C., Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129. (1981) Zbl0487.49027MR0614246
  3. DEGIOVANNI M., Bifurcation for odd nonlinear variational inequalities, Ann. Fac. Sci. Toulouse Math. (6) 11 (1990), 39-66. (1990) MR1191471
  4. DU Y., A deformation lemma and some critical point theorems, Bull. Austral. Math. Soc. 43 (1991), 161-168. (1991) Zbl0714.58008MR1086730
  5. GHOUSSOUB N., A min-max principle with a relaxed boundary condition, Proc. Amer. Math. Soc. 117 (1993), 439-447. (1993) Zbl0791.49028MR1089405
  6. GHOUSSOUB N.-PREISS D., A general mountain pass principle for locating and classifying critical points, Ann. Inst. H. Poincare. Anal. Non Lineaire 6 (1989), 321-330. (1989) Zbl0711.58008MR1030853
  7. HOFER H., A note on the topological degree at a critical point of mountainpath-type, Proc. Amer. Math. Soc. 90 (1984), 309-315. (1984) MR0727256
  8. HULSHOF J.-van der VORST R., Differential systems with strongly indefinite variational structure, J. Funct. Anal. 114 (1993), 97-105. (1993) Zbl0793.35038MR1220982
  9. KAVIAN O., Introduction á la theorie des points critiques et applications aux problémes elliptiques, Mathématiques & Applications 13, Springer Verlag, Paris, 1993. (1993) Zbl0797.58005MR1276944
  10. KUBRULSKI R. S., Variational methods for nonlinear eigenvalue problems, Differential Integral Equations 3 (1990), 923-932. (1990) 
  11. LEFTER C.-MOTREANU D., Critical point theory in nonlinear eigenvalue problems with discontinuities, In.: Internat. Ser. Numer. Math. 107, Birkhäuser Verlag, Basel, 1992, pp. 25-36. (1992) MR1223355
  12. MOTREANU D., Existence for minimization with nonconvex constraints, J. Math. Anal. Appl. 117 (1986), 128-137. (1986) Zbl0599.49008MR0843009
  13. MOTREANU D.-PANAGIOTOPOULOS P. D., Hysteresis: the eigenvalue problem for hemivariational inequalities, In: Models of Hysteresis, Longman Scient. PubL, Harlow, 1993, pp. 102-117. (1993) Zbl0801.49027MR1235118
  14. PALAIS R. S., Lusternik-Schnirelman theory on Banach manifolds, Topology 5 (1966), 115-132. (1966) Zbl0143.35203MR0259955
  15. PALAIS R. S.-TERNG C. L., Critical Point Theory and Submanifold Geometry, Lecture Notes in Math. 1353, Springer Verlag, Berlin, 1988. (1988) Zbl0658.49001MR0972503
  16. RABINOWITZ P. H., Variational methods for nonlinear eigenvalue problems, In: Eigenvalues of Nonlinear Problems (G. Prodi, ed.), C.I.M.E., Edizioni Cremonese, Roma, 1975, pp. 141-195. (1975) MR0464299
  17. RABINOWITZ P. H., Minimax Methods in Critical Point Theory With Applications to Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer.Math.Soc, Providence, R.I., 1986. (1986) Zbl0609.58002MR0845785
  18. RAUCH J., Discontinuous semilinear differential equations and multiple valued maps, Proc. Amer. Math. Soc. 64 (1977), 277-282. (1977) Zbl0413.35031MR0442453
  19. SCHECHTER M.-TINTAREV K., Spherical maxima in Hilbert space and semilinear elliptic eigenvalue problems, Differential Integral Equations 3 (1990), 889-899. (1990) Zbl0727.35105MR1059337
  20. SCHECHTER M.-TINTAREV K., Points of spherical maxima and solvability of semilinear elliptic equations, Canad. J. Math. 43 (1991), 825-831. (1991) Zbl0755.35083MR1127032
  21. SZULKIN A., Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. H. Poincaré Anal. Non Lineaire 3 (1986), 77-109. (1986) Zbl0612.58011MR0837231
  22. SZULKIN A., Ljusternik-Schnirelman theory on C 1 -manifold, Ann. Inst. H. Poincaré Anal Non Linéaire 5 (1988), 119-139. (1988) MR0954468
  23. WANG T., Ljusternik-Schnirelman category theory on closed subsets of Banach manifolds, J. Math. Anal. Appl. 149 (1990), 412-423. (1990) MR1057683
  24. ZEIDLER E., Ljusternik-Schnirelman theory on general level sets, Math. Nachr. 129 (1986), 235-259. (1986) Zbl0608.58014MR0864637

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.