zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Infinitely many weak solutions for a class of quasilinear elliptic systems. (English) Zbl 1201.35102
Summary: We deal with the existence of weak solutions for a quasilinear elliptic system. More precisely the existence of an exactly determined open interval of positive parameters for which the system admits infinitely many weak solutions is established. Our proofs are based on variational methods.
35J65Nonlinear boundary value problems for linear elliptic equations
35D30Weak solutions of PDE
[1]Afrouzi, G. A.; Heidarkhani, S.: Existence of three solutions for a class of Dirichlet quasilinear elliptic systems involving the (p1,,pm)-Laplacian, Nonlinear anal. 70, 135-143 (2009) · Zbl 1161.35371 · doi:10.1016/j.na.2007.11.038
[2]Bartsch, T.; De Figueiredo, D. G.: Infinitely many solutions of nonlinear elliptic systems, Progr. nonlinear differential equations appl. 35, 51-67 (1999) · Zbl 0922.35049
[3]Bensedik, A.; Bouchekif, M.: On certain nonlinear elliptic systems with indefinite terms, Electron. J. Differential equations 83, 1-16 (2002) · Zbl 1068.35507 · doi:emis:journals/EJDE/Volumes/2002/83/abstr.html
[4]Boccardo, L.; De Figueiredo, D. G.: Some remarks on a system of quasilinear elliptic equations, Nonlinear differential equations appl. 9, 309-323 (2002) · Zbl 1011.35050 · doi:10.1007/s00030-002-8130-0
[5]Clément, Ph.; De Figueiredo, D. G.; Mitidieri, E.: Positive solutions of semilinear elliptic systems, Comm. partial differential equations 17, 923-940 (1992) · Zbl 0818.35027 · doi:10.1080/03605309208820869
[6]De Figueiredo, D. G.: Semilinear elliptic systems: A survey of superlinear problems, Resenhas 2, 373-391 (1996) · Zbl 0984.35063
[7]Hai, D. D.; Shivaji, R.: An existence result on positive solutions for a class of p-Laplacian systems, Nonlinear anal. 56, 1007-1010 (2004)
[8]Felmer, P.; Manásevich, R. F.; De Thélin, F.: Existence and uniqueness of positive solutions for certain quasilinear elliptic systems, Comm. partial differential equations 17, 2013-2029 (1992) · Zbl 0813.35020 · doi:10.1080/03605309208820912
[9]Felmer, P.; Wang, Z-Q.: Multiplicity for symmetric indefinite functionals: application to Hamiltonian and elliptic systems, Topol. methods nonlinear anal. 12, No. 2, 207-226 (1998) · Zbl 0931.35044
[10]De Figueiredo, D. G.; Felmer, P. L.: On superquadratic elliptic systems, Trans. amer. Math. soc. 343, 99-116 (1994) · Zbl 0799.35063 · doi:10.2307/2154523
[11]De Figueiredo, D. G.; Magalhães, C. A.: On nonquadratic Hamiltonian elliptic systems, Adv. differential equations 1, No. 5, 881-898 (1996) · Zbl 0857.35043
[12]Li, C.; Tang, C. -L.: Three solutions for a class of quasilinear elliptic systems involving the (p,q)-Laplacian, Nonlinear anal. 69, 3322-3329 (2008) · Zbl 1158.35356 · doi:10.1016/j.na.2007.09.021
[13]Zou, W.; Li, S.; Liu, J. Q.: Nontrivial solutions for resonant cooperative elliptic systems via computations of critical groups, Nonlinear anal. 38, 229-247 (1999) · Zbl 0940.35074 · doi:10.1016/S0362-546X(98)00191-6
[14]Bozhkova, Y.; Mitidieri, E.: Existence of multiple solutions for quasilinear systems via fibering method, J. differential equations 190, 239-267 (2003) · Zbl 1021.35034 · doi:10.1016/S0022-0396(02)00112-2
[15]Zhang, G. Q.; Liu, X. P.; Liu, S. Y.: Remarks on a class of quasilinear elliptic systems involving the (p,q)-Laplacian, Electron. J. Differential equations 2005, 1-10 (2005) · Zbl 1129.35362 · doi:emis:journals/EJDE/Volumes/2005/20/abstr.html
[16]Djellit, A.; Tas, S.: Quasilinear elliptic systems with critical Sobolev exponents in RN, Nonlinear anal. 66, 1485-1497 (2007) · Zbl 1118.35023 · doi:10.1016/j.na.2006.02.005
[17]Breckner, B.; Varga, Cs.: A multiplicity result for gradient-type systems with non-differentiable term, Acta math. Hungar. 118, No. 1–2, 85-104 (2008) · Zbl 1164.47063 · doi:10.1007/s10474-007-6165-8
[18]Cammaroto, F.; Chinnì, A.; Di Bella, B.: Multiple solutions for a quasilinear elliptic variational system on strip-like domains, Proc. edinb. Math. soc. (2) 50, No. 3, 597-603 (2007) · Zbl 1136.35062 · doi:10.1017/S0013091505001380
[19]Kristály, A.: Existence of two non-trivial solutions for a class of quasilinear elliptic variational systems on strip-like domains, Proc. edinb. Math. soc. (2) 48, No. 2, 465-477 (2005) · Zbl 1146.35349 · doi:10.1017/S0013091504000112
[20]Bonanno, G.; Bisci, G. Molica: Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. value probl. 2009, 1-20 (2009) · Zbl 1177.34038 · doi:10.1155/2009/670675
[21]Ricceri, B.: A general variational principle and some of its applications, J. comput. Appl. math. 113, 401-410 (2000) · Zbl 0946.49001 · doi:10.1016/S0377-0427(99)00269-1
[22]Omari, P.; Zanolin, F.: Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential, Comm. partial differential equations 21, No. 5–6, 721-733 (1996) · Zbl 0856.35046 · doi:10.1080/03605309608821205
[23]Talenti, G.: Some inequalities of Sobolev type on two-dimensional spheres, Internat. ser. Numer. math. 80, 401-408 (1987) · Zbl 0652.26020
[24]G. Bonanno, G. Molica Bisci, Infinitely many solutions for a Dirichlet problem involving the p-Laplacian, Proc. Roy. Soc. Edinburgh Sect. A (in press). · Zbl 1197.35125 · doi:10.1017/S0308210509000845
[25]Pucci, P.; Serrin, J.: The strong maximum priciple revisited, J. differential equations 196, 1-66 (2004) · Zbl 1109.35022 · doi:10.1016/j.jde.2004.09.002
[26]Di Falco, A. G.: Infinitely many solutions to the Dirichlet problem for quasilinear elliptic systems, Le matematiche 60, No. Fasc. I, 163-179 (2005) · Zbl 1195.35136