Title:
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Sign-changing solutions and multiplicity results for some quasi-linear elliptic Dirichlet problems (English) |
Author:
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Omana, Rebecca Walo |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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48 |
Issue:
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3 |
Year:
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2007 |
Pages:
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395-415 |
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Category:
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math |
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Summary:
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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. (English) |
Keyword:
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sign-changing |
Keyword:
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mountain-pass theorem |
Keyword:
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ordered intervals |
MSC:
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35J20 |
MSC:
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35J25 |
MSC:
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35J60 |
MSC:
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35J62 |
MSC:
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35J65 |
idZBL:
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Zbl 1199.35104 |
idMR:
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MR2374123 |
. |
Date available:
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2009-05-05T17:03:46Z |
Last updated:
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2012-05-01 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/119668 |
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Reference:
|
[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. MR 1373473 |
Reference:
|
[2] Alama S., Tarantello G.: On semilinear elliptic equations with indefinite nonlinearities.Calc. Var. Partial Differential Equations 1 (1993), 469-475. Zbl 0809.35022, MR 1383913 |
Reference:
|
[3] Amann H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces.SIAM Rev. 18 (1976), 620-709. Zbl 0345.47044, MR 0415432 |
Reference:
|
[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. Zbl 0805.35028, MR 1276168 |
Reference:
|
[5] Ambrosetti A., Azorero J.G., Peral I.: Multiplicity results for some nonlinear elliptic equations.J. Funct. Anal. 137 (1996), 214-242. Zbl 0852.35045, MR 1383017 |
Reference:
|
[6] Ambrosetti A., Azorero J.G., Peral I.: Existence and multiplicity results for some nonlinear elliptic equations.a survey, SISSA preprint 4/2000/M. Zbl 1011.35049, MR 1801341 |
Reference:
|
[7] Arcoya D., Boccardo L.: Some remarks on critical point theory for nondifferentiable functionals.Nonlinear Differential Equations Appl. 6 (1999), 79-100. Zbl 0923.35049, MR 1674782 |
Reference:
|
[8] Arcoya D., Carmona J., Pellacci B.: Bifurcation for some quasi-linear operators.SISSA preprint, 1999. |
Reference:
|
[9] Artola M., Boccardo L.: Positive solutions for some quasi-linear elliptic equations.Comm. Appl. Nonlinear Anal. 3 4 (1996), 89-98. MR 1420287 |
Reference:
|
[10] Chang K.C.: Infinite dimensional Morse theory and multiple solution problems.Birkhäuser, Boston, 1993. Zbl 0779.58005, MR 1196690 |
Reference:
|
[11] Chang K.C.: $H^1$ versus $C^1$ isolated critical points.C.R. Acad. Sci. Paris, Sér. I Math. 319 441-446 (1994). MR 1296769 |
Reference:
|
[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. MR 1458519 |
Reference:
|
[13] de Figueiredo D.G.: Positive solutions of semilinear elliptic problems.in Variational Methods in Analysis and Mathematical Physics, ICTP Trieste autumn course, 1981. Zbl 0506.35038 |
Reference:
|
[14] Mawhin J., Willem M.: Critical point theory and Hamiltonian Systems.Springer, New York, 1989. Zbl 0676.58017, MR 0982267 |
Reference:
|
[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. MR 1785289 |
Reference:
|
[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. MR 1760528 |
Reference:
|
[17] Struwe M.: Variational Methods: Applications to Nonlinear Partial Differential Equation and Hamiltonian Systems.Springer, Berlin, 1990. MR 1078018 |
Reference:
|
[18] Whyburn G.T.: Topological Analysis.Princeton University Press, Princeton, 1958. Zbl 0186.55901, MR 0099642 |
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