Sign-changing solutions and multiplicity results for some quasi-linear elliptic Dirichlet problems

Rebecca Walo Omana

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 3, page 395-415
  • ISSN: 0010-2628

Abstract

top
In this paper we show some results of multiplicity and existence of sign-changing solutions using a mountain pass theorem in ordered intervals, for a class of quasi-linear elliptic Dirichlet problems. As a by product we construct a special pseudo-gradient vector field and a negative pseudo-gradient flow for the nondifferentiable functional associated to our class of problems.

How to cite

top

Omana, Rebecca Walo. "Sign-changing solutions and multiplicity results for some quasi-linear elliptic Dirichlet problems." Commentationes Mathematicae Universitatis Carolinae 48.3 (2007): 395-415. <http://eudml.org/doc/250221>.

@article{Omana2007,
abstract = {In this paper we show some results of multiplicity and existence of sign-changing solutions using a mountain pass theorem in ordered intervals, for a class of quasi-linear elliptic Dirichlet problems. As a by product we construct a special pseudo-gradient vector field and a negative pseudo-gradient flow for the nondifferentiable functional associated to our class of problems.},
author = {Omana, Rebecca Walo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sign-changing; mountain-pass theorem; ordered intervals; sign-changing solutions; quasilinear elliptic equation; mountain pass theorem; multiplicity of solutions},
language = {eng},
number = {3},
pages = {395-415},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sign-changing solutions and multiplicity results for some quasi-linear elliptic Dirichlet problems},
url = {http://eudml.org/doc/250221},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Omana, Rebecca Walo
TI - Sign-changing solutions and multiplicity results for some quasi-linear elliptic Dirichlet problems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 3
SP - 395
EP - 415
AB - In this paper we show some results of multiplicity and existence of sign-changing solutions using a mountain pass theorem in ordered intervals, for a class of quasi-linear elliptic Dirichlet problems. As a by product we construct a special pseudo-gradient vector field and a negative pseudo-gradient flow for the nondifferentiable functional associated to our class of problems.
LA - eng
KW - sign-changing; mountain-pass theorem; ordered intervals; sign-changing solutions; quasilinear elliptic equation; mountain pass theorem; multiplicity of solutions
UR - http://eudml.org/doc/250221
ER -

References

top
  1. Alama S., Del Pino M., Solutions of elliptic equation with indefinite nonlinearities via Morse theory and linking, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), 95-115. (1996) MR1373473
  2. Alama S., Tarantello G., On semilinear elliptic equations with indefinite nonlinearities, Calc. Var. Partial Differential Equations 1 (1993), 469-475. (1993) Zbl0809.35022MR1383913
  3. Amann H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), 620-709. (1976) Zbl0345.47044MR0415432
  4. Ambrosetti A., Brezis H., Cerami G., Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), 519-543. (1994) Zbl0805.35028MR1276168
  5. Ambrosetti A., Azorero J.G., Peral I., Multiplicity results for some nonlinear elliptic equations, J. Funct. Anal. 137 (1996), 214-242. (1996) Zbl0852.35045MR1383017
  6. Ambrosetti A., Azorero J.G., Peral I., Existence and multiplicity results for some nonlinear elliptic equations, a survey, SISSA preprint 4/2000/M. Zbl1011.35049MR1801341
  7. Arcoya D., Boccardo L., Some remarks on critical point theory for nondifferentiable functionals, Nonlinear Differential Equations Appl. 6 (1999), 79-100. (1999) Zbl0923.35049MR1674782
  8. Arcoya D., Carmona J., Pellacci B., Bifurcation for some quasi-linear operators, SISSA preprint, 1999. 
  9. Artola M., Boccardo L., Positive solutions for some quasi-linear elliptic equations, Comm. Appl. Nonlinear Anal. 3 4 (1996), 89-98. (1996) MR1420287
  10. Chang K.C., Infinite dimensional Morse theory and multiple solution problems, Birkhäuser, Boston, 1993. Zbl0779.58005MR1196690
  11. Chang K.C., H 1 versus C 1 isolated critical points, C.R. Acad. Sci. Paris, Sér. I Math. 319 441-446 (1994). (1994) MR1296769
  12. Dancer E.N., and Du Yihong, A note on multiple solutions for some semilinear elliptic problems, J. Math. Anal. Appl. 211 (1997), 626-640. (1997) MR1458519
  13. de Figueiredo D.G., Positive solutions of semilinear elliptic problems, in Variational Methods in Analysis and Mathematical Physics, ICTP Trieste autumn course, 1981. Zbl0506.35038
  14. Mawhin J., Willem M., Critical point theory and Hamiltonian Systems, Springer, New York, 1989. Zbl0676.58017MR0982267
  15. Li. S., Wang Z.Q., Mountain-pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet's problems, J. Anal. Math. 81 (2000), 373-395. (2000) MR1785289
  16. Li S., Zhang Z., Sign-changing solutions ad multiple solution theorems for semilinear elliptic boundary value problems with jumping nonlinearities, Acta Math. Sinica 16 1 (2000), 113-122. (2000) MR1760528
  17. Struwe M., Variational Methods: Applications to Nonlinear Partial Differential Equation and Hamiltonian Systems, Springer, Berlin, 1990. MR1078018
  18. Whyburn G.T., Topological Analysis, Princeton University Press, Princeton, 1958. Zbl0186.55901MR0099642

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.